M. K. Agoston, Algebraic Topology, a first course, Pure and applied mathematics, 1976.

S. Alayrangues, X. Daragon, J. Lachaud, and P. Lienhardt, Equivalence between regular n-G-maps and n-surfaces, 10th Int, Combinatorial Image Analysis, 2004.
DOI : 10.1007/978-3-540-30503-3_10

S. Ansaldi, L. De-floriani, and B. Falcidieno, Geometric modeling of solid objects by using a face adjacency graph representation, ACM SIGGRAPH Computer Graphics, vol.19, issue.3, pp.131-139, 1985.
DOI : 10.1145/325165.325218

D. Arquès and P. Koch, Modélisation de solides par les pavages, Proc. Pixim '89, pp.47-61, 1989.

P. Bandieri, M. R. Casali, and C. Gagliardi, Representing manifolds by crystallization theory: foundations, improvements and related results, Atti. Sem. Mat. Fis. Univ. Modena, vol.49, pp.283-337, 2001.

B. Baumgart, A polyhedron representation for computer vision, Proceedings of the May 19-22, 1975, national computer conference and exposition on, AFIPS '75, pp.589-596, 1975.
DOI : 10.1145/1499949.1500071

G. Bertrand, G. Bertrand, M. Couprie, and L. Perroton, New Notions for Discrete Topology, Proc. DGCI '99, pp.218-228, 1999.
DOI : 10.1007/3-540-49126-0_17
URL : https://hal.archives-ouvertes.fr/hal-00621992

Y. Bertrand, G. Damiand, and C. Fiorio, Topological Encoding of 3D Segmented Images, Proceedings of 9th Discrete Geometry for Computer Imagery, pp.311-324, 1953.
DOI : 10.1007/3-540-44438-6_26
URL : https://hal.archives-ouvertes.fr/lirmm-01168508

Y. Bertrand and J. Dufourd, Algebraic Specification of a 3D-Modeler Based on Hypermaps, CVGIP: Graphical Models and Image Processing, vol.56, issue.1, pp.56-85, 1994.
DOI : 10.1006/cgip.1994.1005

S. Brandel, S. Schneider, M. Perrin, N. Guiard, J. Rainaud et al., Automatic Building of Structured Geological Models, Journal of Computing and Information Science in Engineering, vol.5, issue.2, p.5, 2005.
DOI : 10.1115/1.1884145

A. Braquelaire, G. Damiand, J. Domenger, and F. Vidil, Comparison and Convergence of Two Topological Models for 3D Image Segmentation, Proceedings of 4th IAPR-TC15 Workshop on Graph- Based Representations in Pattern Recognition, pp.59-70, 2003.
DOI : 10.1007/3-540-45028-9_6
URL : https://hal.archives-ouvertes.fr/hal-01513090

J. Braquelaire and P. Guitton, A Model for Image Structuration, Proc. Computer Graphics International '88, 1988.
DOI : 10.1007/978-3-642-83492-9_37

E. Brisson, Representing geometric structures in d dimensions: topology and order, Proc. 5th ACM Symp, pp.218-227, 1989.

E. Brisson, Representing geometric structures in d dimensions: topology and order, Discrete & Computational Geometry, issue.1 9, pp.387-426, 1993.

L. Brun and W. Kropatsch, Combinatorial pyramids, Proceedings 2003 International Conference on Image Processing (Cat. No.03CH37429), pp.33-37, 2003.
DOI : 10.1109/ICIP.2003.1246609
URL : https://hal.archives-ouvertes.fr/hal-00807887

R. Bryant and D. Singerman, Foundations of the Theory of Maps on Surfaces with Boundaries, Quart, Journal of Math. Oxford, issue.2, pp.36-53, 1985.

P. Cavalcanti, P. Carvalho, M. , and L. , Non-manifold modeling: an approach based on spatial subdivisions, Computer-Aided Design, vol.29, issue.3, pp.299-320, 1997.

D. Cazier and J. Dufourd, A rewrite system to build planar subdivisions, Proceedings of the 7th Canadian Conference on Computational Geometry, pp.235-240, 1995.
URL : https://hal.archives-ouvertes.fr/hal-01208572

X. Chen and P. Lienhardt, Modeling and Programming Evolutions of Surfaces, Computer Graphics Forum, vol.2, issue.5, pp.323-341, 1992.

P. Cigogni, L. De-floriani, C. Montani, E. Puppo, and R. Scopigno, Multiresolution modeling and visualization of volume data based on simplicial complexes, Symposium on, vol.Visualization, pp.19-26, 1994.

R. Cori, Un code pour les graphes planaires et ses applications, Astérisque, vol.27, 1975.

G. Crocker and W. Reinke, An Editable Non-Manifold Boundary Representation, Computer Graphics and Applications, issue.2, p.11, 1991.
DOI : 10.1109/38.75589

F. H. Croom, Basic Concepts of Algebraic Topology, 1978.
DOI : 10.1007/978-1-4684-9475-4

W. Dahmen and C. A. Micchelli, -Splines, I. Triangulations of Simploids, SIAM Journal on Numerical Analysis, vol.19, issue.5, pp.993-1012, 1982.
DOI : 10.1137/0719072
URL : https://hal.archives-ouvertes.fr/hal-00773474

G. Damiand, Y. Bertrand, and C. Fiorio, Topological model for two-dimensional image representation: definition and optimal extraction algorithm, Computer Vision and Image Understanding, vol.93, issue.2, pp.93-111, 2004.
DOI : 10.1016/j.cviu.2003.09.001
URL : https://hal.archives-ouvertes.fr/lirmm-00137917

G. Damiand and P. Lienhardt, Removal and Contraction for N - Dimensional Generalized Maps, 11th Discrete Geometry for Computer Imagery, pp.408-419, 2003.

X. Daragon, M. Couprie, B. , and G. , Discrete Frontiers, Proc. DGCI'03, pp.236-245, 2003.
DOI : 10.1007/978-3-540-39966-7_22
URL : https://hal.archives-ouvertes.fr/hal-00622040

D. Floriani, L. Falcidieno, and B. , A hierarchical boundary model for solid object representation, ACM Transactions on Graphics, vol.7, issue.1, pp.42-60, 1988.
DOI : 10.1145/42188.46164

D. Floriani, L. Magillo, P. Puppo, E. Sobrero, and D. , A multiresolution topological representation for non-manifold meshes, Computer-Aided Design, issue.2, pp.36-141, 2004.

D. Floriani, L. Mesmoudi, M. Morando, F. Puppo, and E. , Decomposing non-manifold objects in arbitrary dimensions, Graphical Models, vol.65, issue.1-3, pp.65-67, 2003.
DOI : 10.1016/S1524-0703(03)00006-7

D. Floriani, L. Morando, F. Puppo, and E. , A Representation for Abstract Simplicial Complexes: An Analysis and a Comparison, Proc. of DGCI '03, pp.454-464, 2003.
DOI : 10.1007/978-3-540-39966-7_43

D. Floriani, L. Morando, F. Puppo, and E. , Representation of non-manifold objects through decomposition into nearly manifold parts, 8th A.C.M. Symposium on Solid Modeling and Applications, pp.304-309, 2003.

D. Floriani, L. Puppo, E. Magillo, and P. , A formal approach to multiresolution hypersurface modelling, Geometric Modeling: Theory and Practice, 1997.

C. J. Delfinado and H. Edelsbrunner, An incremental algorithm for Betti numbers of simplicial complexes on the 3-sphere, Computer Aided Geometric Design, vol.12, issue.7, pp.771-784, 1995.
DOI : 10.1016/0167-8396(95)00016-Y

T. Derose, Composing B??zier simplexes, ACM Transactions on Graphics, vol.7, issue.3, pp.198-221, 1988.
DOI : 10.1145/44479.44482

T. Dey, H. Edelsbrunner, and S. Guha, Computational topology, Advances in Discrete and Computational Geometry, Contemporary mathematics 223, pp.109-143, 1999.
DOI : 10.1090/conm/223/03135

D. Dobkin and M. Laszlo, Primitives for the Manipulation of Three- Dimensional Subdivisions, 3rd Symposium on Computational Geometry, pp.86-99, 1987.

D. Dobkin and M. Laszlo, Primitives for the Manipulation of Three- Dimensional Subdivisions, Algorithmica, vol.5, issue.4, pp.3-32, 1989.

J. Dufourd, Formal specification of topological subdivisions using hypermaps, Computer-Aided Design, vol.23, issue.2, pp.99-116, 1991.
DOI : 10.1016/0010-4485(91)90001-D

J. Dufourd, Algebras and formal specifications in geometric modelling, The Visual Computer, vol.13, issue.3, pp.131-154, 1997.
DOI : 10.1007/s003710050095

J. Edmonds, A Combinatorial Representation for Polyhedral Surfaces, Notices Amer, Math. Soc, vol.7, 1960.

H. Elter and P. Lienhardt, Different combinatorial models based on the map concept for the representation of different types of cellular complexes, Proceedings of IFIP TC 5/WG II Working Conference on Geometric Modeling in Computer Graphics, 1993.

H. Elter and P. Lienhardt, CELLULAR COMPLEXES AS STRUCTURED SEMI-SIMPLICIAL SETS, International Journal of Shape Modeling, vol.01, issue.02, pp.191-217, 1994.
DOI : 10.1142/S021865439400013X

G. Farin, Curves and Surfaces for Computer Aided Geometric Design: A Practical guide, 2001.

M. Ferri and C. Gagliardi, Crystallisation moves, Pacific Journal of Mathematics, vol.100, issue.1, pp.85-103, 1982.
DOI : 10.2140/pjm.1982.100.85

M. Ferri, C. Gagliardi, and L. Grasselli, A graph-theoretical representation of PL-manifolds ??? A survey on crystallizations, Aequationes Mathematicae, vol.20, issue.2, pp.31-121, 1986.
DOI : 10.1007/BF02188181

V. Ferruci and A. Paoluzzi, Extrusion and boundary evaluation for multidimensional polyhedra, Computer-Aided Design, vol.23, issue.11, pp.40-50, 1991.
DOI : 10.1016/0010-4485(91)90098-H

C. Fiorio, A topologically consistent representation for image analysis: The Frontiers Topological Graph, Proc. of DGCI '96, pp.151-162, 1996.
DOI : 10.1007/3-540-62005-2_13
URL : https://hal.archives-ouvertes.fr/lirmm-01168321

D. Fradin, D. Meneveaux, and P. Lienhardt, A Hierarchical Topology-Based Model for Handling Complex Indoor Scenes, Computer Graphics Forum, vol.21, issue.8, 2006.
DOI : 10.1145/882262.882324
URL : https://hal.archives-ouvertes.fr/hal-00332648

R. Fritsch and R. Piccinini, Cellular Structures in Topology, 1990.
DOI : 10.1017/CBO9780511983948

L. Fuchs, D. Bechmann, Y. Bertrand, and J. Dufourd, Formal specification for free-form curves and surfaces, Proceedings of Spring Conference on Computer Graphics, 1996.

L. Fuchs and P. Lienhardt, Topological structures for d-dimensional free-form objects, Proceedings of Computer-Aided Geometric Design '97, 1997.

C. Gagliardi, How to deduce the fundamental group of a closed nmanifold from a contracted triangulation, Journal of Combinatorics, Information and System Sciences, vol.4, issue.3, pp.237-252, 1979.

C. Gagliardi, Regular imbeddings of edge-coloured graphs, Geometriae Dedicata, vol.11, issue.4, pp.397-414, 1981.
DOI : 10.1007/BF00181201

R. González-díaz and P. Real, Towards Digital Cohomology, Proc. DGCI'2003, pp.92-101, 2003.
DOI : 10.1007/978-3-540-39966-7_8

L. Guibas and G. Stolfi, Primitives for the manipulation of general subdivisions and the computation of Voronoi diagrams, Proceedings of the fifteenth annual ACM symposium on Theory of computing , STOC '83, pp.74-123, 1985.
DOI : 10.1145/800061.808751

E. L. Gursoz and F. Prinz, Vertex-based Representation of Non- Manifolds Boundaries, Geometric Modeling for Product Engineering, pp.107-130, 1990.

O. Hansen and N. Christiansen, A model for n-dimensional boundary topology, Proceedings on the second ACM symposium on Solid modeling and applications , SMA '93, pp.65-73, 1993.
DOI : 10.1145/164360.164386

L. James, Maps and Hypermaps: Operations and Symmetry, 1985.

J. Jolion and A. Montanvert, The adaptive pyramid: A framework for 2D image analysis, CVGIP: Image Understanding, vol.55, issue.3, pp.339-348, 1992.
DOI : 10.1016/1049-9660(92)90031-W

W. Kropatsch, Building irregular pyramids by dual-graph contraction, Vision, image and signal processing, pp.366-374, 1995.

T. Kunii and S. Takahashi, Area Guide Map Modeling by Manifolds and CW-Complexes, Proc. IFIP TC 5/WG 2 Working Conf. on Geometric Modeling in Computer Graphics, pp.5-20, 1993.
DOI : 10.1007/978-3-642-78114-8_1

V. Lang and P. Lienhardt, Geometric modeling with simplicial sets, Proceedings of Pacific Graphics '95, 1995.

V. Lang and P. Lienhardt, Simplicial sets and triangular patches, Proceedings of CG International '96, 1996.
DOI : 10.1109/CGI.1996.511797

S. Lee and K. Lee, Partial entity structure, Proceedings of the sixth ACM symposium on Solid modeling and applications , SMA '01, 2001.
DOI : 10.1145/376957.376976

P. Lienhardt, Free-Form Surfaces Modeling by Evolution Simulation, Proc. Eurographics '88, pp.327-341, 1988.

P. Lienhardt, -dimensional generalized maps, Proceedings of the fifth annual symposium on Computational geometry , SCG '89, pp.228-236, 1989.
DOI : 10.1145/73833.73859
URL : https://hal.archives-ouvertes.fr/hal-00909382

P. Lienhardt, Subdivisions of Surfaces and Generalized Maps, Proc. Eurographics '89, pp.439-452, 1989.

P. Lienhardt, Topological models for boundary representation: a comparison with n-dimensional generalized maps, Computer-Aided Design, vol.23, issue.11, pp.59-82, 1991.
DOI : 10.1016/0010-4485(91)90100-B

P. Lienhardt, N-DIMENSIONAL GENERALIZED COMBINATORIAL MAPS AND CELLULAR QUASI-MANIFOLDS, International Journal of Computational Geometry & Applications, vol.04, issue.03, pp.275-324, 1994.
DOI : 10.1142/S0218195994000173

P. Lienhardt, X. Skapin, and A. Bergey, CARTESIAN PRODUCT OF SIMPLICIAL AND CELLULAR STRUCTURES, International Journal of Computational Geometry & Applications, vol.14, issue.03, pp.115-159, 2004.
DOI : 10.1142/S0218195904001408

S. Lins, Gems, computers and attractors for 3-manifolds, Series on Knots and Everything 5, World Scientific, 1995.

S. Lins and A. Mandel, Graph-encoded 3-manifolds, Discrete Mathematics, vol.57, issue.3, pp.261-284, 1985.
DOI : 10.1016/0012-365X(85)90179-7
URL : http://doi.org/10.1016/0012-365x(85)90179-7

Y. Luo and G. Lukacs, A boundary representation for form features and non-manifold solid objects, Proceedings of the first ACM symposium on Solid modeling foundations and CAD/CAM applications , SMA '91, 1990.
DOI : 10.1145/112515.112527

M. Mäntylä, Computational Topology: a Study of Topological Manipulations and Interrogations in Computer Graphics and Geometric Modeling, Acta Polytechnica Scandinavia, vol.37, 1983.

M. Mäntylä, An Introduction to Solid Modeling, 1988.

M. Mäntylä and R. Sulonen, GWB: A Solid Modeler with Euler Operators, IEEE Computer Graphics and Applications, vol.2, issue.7, pp.17-31, 1982.
DOI : 10.1109/MCG.1982.1674396

J. P. May, Simplicial objects in algebraic topology, 1967.

H. Meine and U. Köthe, The GeoMap: A Unified Representation for Topology and Geometry, Proc. IAPR Graph-based representations in pattern recognition, 2005.
DOI : 10.1007/978-3-540-31988-7_12

A. Montanvert, P. Meer, and A. Rosenfeld, Hierarchical Image Analysis Using Irregular Tessellations, pp.307-316, 1991.
DOI : 10.1109/34.88566

D. Moore, Graphic Gems III, chapter, 10 Understanding simploids, pp.250-255, 1992.

S. Murabata and M. Higashi, Non-manifold geometric modeling for set operations and surface operations, Proc. IFIP/RPI Geometric Modeling Conference, 1990.

M. Niethammer, A. Stein, W. Kalies, P. Pilarczyk, K. Mischaikow et al., Analysis of blood vessel topology by cubical homology, Proceedings. International Conference on Image Processing, pp.969-972, 2002.
DOI : 10.1109/ICIP.2002.1040114

A. Paoluzzi, F. Bernardini, C. Cattani, and V. Ferrucci, Dimension-independent modeling with simplicial complexes, ACM Transactions on Graphics, vol.12, issue.1, pp.12-56, 1993.
DOI : 10.1145/169728.169719

V. Pascucci, V. Ferrucci, and A. Paoluzzi, Dimensionindependent convex-cell based hierarchical polyhedral complex: representation scheme and implementation issues, 3rd Symposium on Solid Modeling and Applications, pp.163-174, 1995.

S. Peltier, S. Alayrangues, L. Fuchs, and J. Lachaud, Computation of homology groups and generators, Computers and graphics, 2006.

S. Peltier, L. Fuchs, and P. Lienhardt, Homology of Simploidal Set, Lecture Notes in Computer Science, vol.4245, pp.235-246, 2006.
DOI : 10.1007/11907350_20

S. Prat, P. Gioia, Y. Bertrand, and D. Meneveaux, Connectivity compression in an arbitrary dimension, The Visual Computer, vol.21, issue.8-10, pp.876-885, 2005.
DOI : 10.1007/s00371-005-0325-z

J. Rossignac, O. Connor, and M. , SGC: A Dimension-Independant Model for Pointsets with Internal Structures and Incomplete boundaries, Geometric modeling for Product Engineering, pp.145-180, 1989.

J. P. Serre, Homologie Singuliere Des Espaces Fibres, The Annals of Mathematics, vol.54, issue.3, pp.425-505, 1951.
DOI : 10.2307/1969485

C. Simon, G. Damiand, and P. Lienhardt, D generalized map pyramids: Definition, representations and basic operations, Pattern Recognition, vol.39, issue.4, pp.527-538, 2006.
DOI : 10.1016/j.patcog.2005.10.004

C. Sobhanpanah, Extension of a boundary representation technique for the description of N dimensional polytopes, Computers & Graphics, vol.13, issue.1, pp.17-23, 1989.
DOI : 10.1016/0097-8493(89)90032-0

J. Spehner, Merging in maps and in pavings, Theoretical Computer Science, vol.86, issue.2, pp.205-232, 1991.
DOI : 10.1016/0304-3975(91)90018-W

W. Tutte, Graph Theory, Encyclopaedia of Mathematics and its Applications, 1984.

A. Vince, Combinatorial maps, Journal of Combinatorial Theory, Series B, vol.34, issue.1, pp.1-21, 1983.
DOI : 10.1016/0095-8956(83)90002-3

K. Weiler, Edge-Based Data Structures for Solid Modeling in Curved-Surface Environments, IEEE Computer Graphics and Applications, vol.5, issue.1, pp.21-40, 1985.
DOI : 10.1109/MCG.1985.276271

K. Weiler, Boundary Graph Operators for Non-Manifold Geometric Modeling Topology Representations, Proc. IFIP WG 5.2 Working Conference, 1986.

K. Weiler, The Radial-Edge Data Structure: A Topological Representation for Non-Manifold Geometry Boundary Modeling, Proc. IFIP WG 5.2 Working Conference, 1986.