, Pseudodifferential operators on manifolds with a Lie structure at infinity, vol.165, pp.717-747, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00098401
On the geometry of Riemannian manifolds with a Lie structure at infinity, Int. J. Math. and Math. Sciences, vol.4, pp.161-193 ,
The analytic index of elliptic pseudodifferential operators on a singular foliation, J. K-Theory, vol.8, issue.3, pp.363-385, 2011. ,
The index of elliptic operators I, Ann. of Math, vol.87, issue.2, pp.484-530, 1968. ,
, of Proceedings of Symposia in Pure Mathematics, vol.38, pp.117-173, 1982.
, Operator algebras and K-theory, pp.1-31, 1981.
On the equivalence of geometric and analytic K-homology, Pure Appl. Math. Q, vol.3, issue.1, pp.1-24, 2007. ,
,
Getzler rescaling via adiabatic deformation and a renormalized index formula, J. Math. Pures Appl ,
Index theory, eta forms, and Deligne cohomology, Mem. Amer. Math. Soc, vol.198, issue.928, 2009. ,
A K-theoretic relative index theorem and Callias-type Dirac operators, Math. Ann, vol.303, issue.2, pp.241-279, 1995. ,
Geometric obstructions for Fredholm boundary conditions for manifolds with corners, Ann. K-Theory, vol.3, issue.3, pp.523-563, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-01490931
Geometric Baum-Connes assembly map for twisted differentiable stacks, Ann. Sci. Éc. Norm. Supér, issue.4, pp.277-323, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-02011004
A survey of foliations and operator algebras, Operator algebras and applications, Part I, pp.521-628, 1982. ,
, A. Connes Connes, Alain. Noncommutative geometry, 1994.
Fredholm criteria for pseudodifferential operators and induced representations of groupoid algebras, Electron. Res. Announc. Math. Sci, vol.24, pp.68-77, 2017. ,
Integrability of Lie brackets, Ann. of Math, issue.2, pp.575-620, 2003. ,
Holonomy groupoids of singular foliations, J. Differential Geom, vol.58, issue.3, pp.467-500, 2001. ,
Lescure, K-duality for stratified pseudomanifolds, Geom. Topol, vol.13, issue.1, pp.49-86, 2009. ,
Groupoids and an index theorem for conical pseudo-manifolds, J. Reine Angew. Math, vol.628, pp.1-35, 2009. ,
URL : https://hal.archives-ouvertes.fr/hal-00094949
, Pseudodifferential operators on manifolds with fibred corners, vol.65, pp.1799-1880, 2015.
DOI : 10.5802/aif.2974
URL : http://www.numdam.org/article/AIF_2015__65_4_1799_0.pdf
, Blowup constructions for Lie groupoids and a Boutet de Monvel type calculus
Lie groupoids, exact sequences, Connes-Thom elements, connecting maps and index maps ,
DOI : 10.1016/j.geomphys.2018.03.012
Bivariant K-theory via correspondences, Adv. Math, vol.225, issue.5, pp.2883-2919, 2010. ,
DOI : 10.1016/j.aim.2010.04.024
URL : https://doi.org/10.1016/j.aim.2010.04.024
Dualities in equivariant Kasparov theory, New York J. Math, vol.16, pp.245-313, 2010. ,
Morphismes K-orientés d'espaces de feuilles et fonctorialité en théorie de Kasparov (d'après une conjecture d'A. Connes). (French) [[K-oriented morphisms of spaces of leaves and functoriality in Kasparov theory, Ann. Sci. École Norm. Sup, issue.4, pp.325-390, 1987. ,
DOI : 10.24033/asens.1537
URL : http://www.numdam.org/article/ASENS_1987_4_20_3_325_0.pdf
, Classics in Mathematics, 2008.
Pseudodifferential analysis on continuous family groupoids, Doc. Math, vol.5, pp.625-655, 2000. ,
Analysis of geometric operators on open manifolds: a groupoid approach. Quantization of singular symplectic quotients, Progr. Math, pp.181-229, 2001. ,
Théorie de Kasparov équivariante et groupoides. I. (French) [Equivariant Kasparov theory and groupoids. I], K-Theory, vol.16, pp.361-390, 1999. ,
, Fredholm perturbations of Dirac operators on manifolds with corners, 2003.
, General theory of Lie groupoids and Lie algebroids, vol.213, 2005.
DOI : 10.1017/cbo9781107325883
, Differential analysis on manifolds with corners
Groupoids and pseudodifferential calculus on manifolds with corners, J. Funct. Anal, vol.199, issue.1, pp.243-286, 2003. ,
DOI : 10.1016/s0022-1236(02)00038-1
URL : https://doi.org/10.1016/s0022-1236(02)00038-1
A topological index theorem for manifolds with corners, Compos. Math, vol.148, issue.2, pp.640-668, 2012. ,
DOI : 10.1112/s0010437x11005458
URL : https://hal.archives-ouvertes.fr/hal-00007727
Indice analytique et groupoides de Lie, C. R. Acad. Sci. Paris Ser. I Math, vol.325, issue.2, pp.193-198, 1997. ,
DOI : 10.1016/s0764-4442(97)84598-3
Equivalence and isomorphism for groupoid C * -algebras, J. Operator Theory, vol.17, issue.1, pp.3-22, 1987. ,
Pseudodifferential operators on non-compact manifolds and analysis on polyhedral domains, Contemp. Math, vol.366, pp.307-328, 2005. ,
DOI : 10.1090/conm/366/06734
, Desingularization of Lie groupoids and pseudodifferential operators on singular spaces
DOI : 10.4310/cag.2019.v27.n1.a5
URL : http://arxiv.org/pdf/1512.08613
Analysis on singular spaces: Lie manifolds and operator algebras, J. Geom. Phys, vol.105, pp.75-101, 2016. ,
DOI : 10.1016/j.geomphys.2016.03.014
URL : https://hal.archives-ouvertes.fr/hal-01285202
Pseudodifferential operators on differential groupoids, Pacific J. Math, vol.189, issue.1, pp.117-152, 1999. ,
, Continuous family groupoids, Homology, Homotopy and Applications, vol.2, pp.89-104, 2000.
Elliptic operators on manifolds with singularities and K-homology, K-theory, vol.34, pp.71-98, 2005. ,
On the strong ext bifunctor, 1983. ,
Unbounded pseudodifferential calculus on Lie groupoids, J. Funct. Anal, vol.236, issue.1, pp.161-200, 2006. ,
, Adiabatic groupoids and secondary invariants in K-theory