D. Attali and A. Lieutier, Optimal Reconstruction Might be Hard, Discrete & Computational Geometry, vol.39, issue.1???3, pp.133-156, 2013.
DOI : 10.1007/s00454-012-9475-8

URL : https://hal.archives-ouvertes.fr/hal-00468602

D. Attali, A. Lieutier, and D. Salinas, Vietoris-rips complexes also provide topologically correct reconstructions of sampled shapes, Proceedings of the 27th annual ACM symposium on Computational geometry, SoCG '11, pp.448-465, 2013.
DOI : 10.1145/1998196.1998276

URL : https://hal.archives-ouvertes.fr/hal-00579864

P. Bendich, H. Edelsbrunner, D. Morozov, and A. Patel, Homology and robustness of level and interlevel sets. Homology, Homotopy and Applications, pp.51-72, 2013.

P. Bubenik and J. Scott, Categorification of Persistent Homology, Discrete & Computational Geometry, vol.33, issue.2, 2014.
DOI : 10.1007/s00454-014-9573-x

F. Chazal and A. Lieutier, Stability and Computation of Topological Invariants of Solids in ${\Bbb R}^n$, Discrete & Computational Geometry, vol.37, issue.4, pp.601-617, 2007.
DOI : 10.1007/s00454-007-1309-8

F. Chazal and A. Lieutier, Smooth manifold reconstruction from noisy and non-uniform approximation with guarantees, Computational Geometry, vol.40, issue.2, pp.156-170, 2008.
DOI : 10.1016/j.comgeo.2007.07.001

URL : https://hal.archives-ouvertes.fr/hal-00864487

F. Chazal, D. Cohen-steiner, and A. Lieutier, A Sampling Theory for Compact Sets in Euclidean Space, Discrete & Computational Geometry, vol.18, issue.3, pp.461-479, 2009.
DOI : 10.1007/s00454-009-9144-8

URL : https://hal.archives-ouvertes.fr/hal-00864493

F. Chazal, V. De-silva, M. Glisse, and S. Oudot, The structure and stability of persistence modules, 2012.
DOI : 10.1007/978-3-319-42545-0

URL : https://hal.archives-ouvertes.fr/hal-01107617

D. Cohen-steiner, H. Edelsbrunner, and D. Morozov, Vines and vineyards by updating persistence in linear time, Proceedings of the twenty-second annual symposium on Computational geometry , SCG '06, pp.119-126, 2006.
DOI : 10.1145/1137856.1137877

D. Cohen-steiner, H. Edelsbrunner, and J. Harer, Stability of Persistence Diagrams, Discrete & Computational Geometry, vol.37, issue.1, pp.103-120, 2007.
DOI : 10.1007/s00454-006-1276-5

D. Cohen-steiner, H. Edelsbrunner, and J. Harer, Extending Persistence Using Poincar?? and Lefschetz Duality, Foundations of Computational Mathematics, vol.33, issue.1, pp.79-103, 2008.
DOI : 10.1007/s10208-008-9027-z

V. De-silva and G. Carlsson, Topological estimation using witness complexes, Eurographics Symposium on Point-Based Graphics, pp.157-166, 2004.

H. Edelsbrunner, Alpha shapes ? a survey, Tessellations in the Sciences: Virtues, Techniques and Applications of Geometric Tilings

H. Edelsbrunner and M. Kerber, Alexander duality for functions, Proceedings of the 2012 symposuim on Computational Geometry, SoCG '12, pp.249-258, 2012.
DOI : 10.1145/2261250.2261287

H. Edelsbrunner, D. Letscher, and A. Zomorodian, Topological Persistence and Simplification, Discrete & Computational Geometry, vol.28, issue.4, pp.511-533, 2002.
DOI : 10.1007/s00454-002-2885-2

H. Edelsbrunner, D. Morozov, and A. Patel, Quantifying Transversality by Measuring the??Robustness of Intersections, Foundations of Computational Mathematics, vol.62, issue.3, pp.345-361, 2011.
DOI : 10.1007/s10208-011-9090-8

A. Hatcher, Algebraic Topology, 2002.

N. Milosavljevi´cmilosavljevi´c, D. Morozov, and P. Skraba, Zigzag persistent homology in matrix multiplication time, Proceedings of the twenty-seventh annual symposium on Computational geometry, pp.216-225, 2011.

D. Morozov, Homological Illusions of Persistence and Stability, 2008.

P. Niyogi, S. Smale, and S. Weinberger, Finding the Homology of Submanifolds with High Confidence from??Random??Samples, Discrete & Computational Geometry, vol.33, issue.11, pp.419-441, 2008.
DOI : 10.1007/s00454-008-9053-2

E. H. Spanier, Algebraic Topology, 1994.
DOI : 10.1007/978-1-4684-9322-1