K. A. , A. , and B. Benedetti, On the embeddability of contractible complexes, Research Report, 2014.

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
DOI : 10.1016/j.comgeo.2012.02.009
URL : https://hal.archives-ouvertes.fr/hal-00785072

D. Attali, A. Lieutier, and D. Salinas, Collapsing Rips complexes, EuroCG'13, 2013.

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

D. W. Barnette and A. Edelson, All 2-manifolds have finitely many minimal triangulations, Israel Journal of Mathematics, vol.30, issue.1, pp.123-128, 1989.
DOI : 10.1007/BF02764905

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

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

G. Carlsson, T. Ishkhanov, A. Vin-de-silva, and . Zomorodian, On the Local Behavior of Spaces of Natural Images, International Journal of Computer Vision, vol.265, issue.4, pp.1-1210, 2008.
DOI : 10.1007/BF00188924

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. Marshall and . Cohen, A course in simple-homotopy theory, Graduate Texts in Mathematics, vol.10, pp.10-1007, 1973.

A. Császár, A polyhedron without diagonals, Acta Sci. Math, vol.13, issue.11, pp.140-142, 1949.

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.157-166157, 2004.

K. Tamal, H. Dey, S. Edelsbrunner, D. V. Guha, and . Nekhayev, Topology preserving edge contraction, Publ. Inst. Math. (Beograd) (N.S.), 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 and P. S. 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://www.cs.caltech.edu/~cs175/cs175-01/resources/GarlandHeckbert2.pdf

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

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

S. Melikhov, Combinatorics of embeddings, 2011.

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
URL : http://arxiv.org/pdf/math/0602531

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.419-44110, 2008.
DOI : 10.1007/b97315

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

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

M. Tancer, Recognition of collapsible complexes is np-complete. Discrete & Computational Geometry, pp.21-38, 2016.

I. A. Volodin, V. E. Kuznetsov, and A. T. Fomenko, THE PROBLEM OF DISCRIMINATING ALGORITHMICALLY THE STANDARD THREE-DIMENSIONAL SPHERE, Russian Mathematical Surveys, vol.29, issue.5, p.7110, 1070.
DOI : 10.1070/RM1974v029n05ABEH001296