D. Attali, A. Lieutier, and D. Salinas, Vietoris???Rips complexes also provide topologically correct reconstructions of sampled shapes, Computational Geometry, vol.46, issue.4, pp.448-465, 2012.
DOI : 10.1016/j.comgeo.2012.02.009
URL : https://hal.archives-ouvertes.fr/hal-00579864

D. W. Barnette and A. Edelson, All orientable 2-manifolds have finitely many minimal triangulations, Israel Journal of Mathematics, vol.33, issue.1, pp.90-98, 1988.
DOI : 10.1007/BF02767355

R. H. Bing, Some Aspects of the Topology of 3-Manifolds Related to the Poincaré Conjecture, In Lectures on Modern Mathematics, 1964.

G. Carlsson and V. Silva, Topological approximation by small simplicial complexes, 2003.

G. Carlsson, T. Ishkhanov, V. D. Silva, and A. Zomorodian, On the Local Behavior of Spaces of Natural Images, International Journal of Computer Vision, vol.265, issue.4, pp.1-12, 2008.
DOI : 10.1007/s11263-007-0056-x

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

M. M. Cohen, A course in simple-homotopy theory, Graduate Texts in Mathematics, vol.10, 1973.
DOI : 10.1007/978-1-4684-9372-6

S. Vin-de, A weak characterisation of the Delaunay triangulation, Geometriae Dedicata, vol.135, issue.1, pp.39-64, 2008.

V. De, S. , and G. Carlsson, Topological estimation using witness complexes, Proceedings of the First Eurographics conference on Point-Based Graphics, pp.157-166, 2004.

T. K. Dey, H. Edelsbrunner, S. Guha, and D. V. Nekhayev, Topology preserving edge contraction, Publ. Inst. Math. (Beograd), vol.66, pp.23-45, 1999.

R. Ehrenborg and G. Hetyei, The topology of the independence complex, European Journal of Combinatorics, vol.27, issue.6, pp.906-923, 2006.
DOI : 10.1016/j.ejc.2005.04.010

M. Garland, S. Paul, and . Heckbert, Surface simplification using quadric error metrics, Proceedings of the 24th annual conference on Computer graphics and interactive techniques , SIGGRAPH '97, pp.209-216, 1997.
DOI : 10.1145/258734.258849
URL : http://cdserver.icemt.iastate.edu/cd/s97cp/contents/papers/garland/quadrics.pdf

X. Goaoc, Transversal Helly numbers, pinning theorems and projections of simplicial complexes, 2011.

H. Hoppe, Progressive meshes, Proceedings of the 23rd annual conference on Computer graphics and interactive techniques , SIGGRAPH '96, pp.99-108, 1996.
DOI : 10.1145/237170.237216

S. Lawrencenko, Irreducible triangulations of the torus, Journal of Mathematical Sciences, vol.51, pp.2537-2543, 1990.

S. Melikhov, Combinatorics of embeddings

E. Nevo, Higher minors and van Kampen's obstruction, MATHEMATICA SCANDINAVICA, vol.101, issue.2, pp.161-176, 2006.
DOI : 10.7146/math.scand.a-15037

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

J. Popovi´cpopovi´c and H. Hoppe, Progressive simplicial complexes, SIG- GRAPH'97 proc, pp.217-224, 1997.

T. Sulanke, Irreducible triangulations of low genus surfaces, Research Report arXiv, 2006.

M. Tancer, Recognition of Collapsible Complexes is NP-Complete, Discrete & Computational Geometry, vol.26, issue.3
DOI : 10.1007/s00454-015-9747-1

I. Volodin, A. T. Ve-kuznetsov, and . Fomenko, THE PROBLEM OF DISCRIMINATING ALGORITHMICALLY THE STANDARD THREE-DIMENSIONAL SPHERE, Russian Mathematical Surveys, vol.29, issue.5, p.71, 1974.
DOI : 10.1070/RM1974v029n05ABEH001296