M. K. Agoston, Algebraic topology: a first course, 1976.

S. Alayrangues, G. Damiand, L. Fuchs, P. Lienhardt, and S. Peltier, Homology computation on cellular structures in image context, in: CTIC, Austria, pp.19-28, 2009.

D. Boltcheva, S. Merino, J. C. Léon, and F. Hétroy, Constructive Mayer-Vietoris algorithm: computing the homology of unions of simplicial complexes, 2010.
URL : https://hal.archives-ouvertes.fr/inria-00542717

C. Chen and D. Freedman, Measuring and computing natural generators for homology groups, Computational Geometry, vol.43, issue.2, pp.169-181, 2010.
DOI : 10.1016/j.comgeo.2009.06.004
URL : http://doi.org/10.1016/j.comgeo.2009.06.004

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

G. Damiand, S. Peltier, and L. Fuchs, Computing Homology for Surfaces with Generalized Maps: Application to 3D Images, pp.235-244, 2006.
DOI : 10.1007/11919629_25
URL : https://hal.archives-ouvertes.fr/hal-00366105

D. Floriani, L. Hui, A. Panozzo, D. Canino, and D. , A Dimension-Independent Data Structure for Simplicial Complexes, pp.403-420, 2010.
DOI : 10.1007/978-3-642-15414-0_24

D. Floriani, L. Mesmoudi, M. M. Morando, F. Puppo, and E. , Decomposing non-manifold objects in arbitrary dimensions, Graphical Models, vol.65, issue.1-3, pp.2-22, 2003.
DOI : 10.1016/S1524-0703(03)00006-7

C. J. Delfinado and H. Edelsbrunner, An incremental algorithm for Betti numbers of simplicial complexes, Proceedings of the ninth annual symposium on Computational geometry , SCG '93, pp.232-239, 1993.
DOI : 10.1145/160985.161140

T. K. Dey and S. Guha, Computing homology groups of simplicial complexes in R3, Proc. 28th ACM Symp. Comp. Theory, 1996.
DOI : 10.1145/274787.274810

T. K. Dey, K. Li, J. Sun, and D. Cohen-steiner, Computing geometry-aware handle and tunnel loops in 3d models, ACM Transactions on Graphics, vol.27, issue.45, 2008.

T. K. Dey, J. Sun, and Y. Wang, Approximating loops in a shortest homology basis from point data, Proceedings of the 2010 annual symposium on Computational geometry, SoCG '10, pp.166-175, 2010.
DOI : 10.1145/1810959.1810989

X. Dousson, J. Rubio, F. Sergeraert, and Y. Siret, The kenzo program, 2008.

J. G. Dumas, F. Heckenbach, B. D. Saunders, and V. Welker, Computing Simplicial Homology Based on Efficient Smith Normal Form Algorithms, Alg., Geom., and Soft. Syst, pp.177-207, 2003.
DOI : 10.1007/978-3-662-05148-1_10
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.7.5885

H. Edelsbrunner and J. Harer, Computational topology, an introduction, AMS, 2010.

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
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.12.8802

B. Fabio, C. Landi, and F. Medri, Recognition of Occluded Shapes Using Size Functions, pp.642-651, 2009.
DOI : 10.1109/99.641604

R. Forman, Morse Theory for Cell Complexes, Advances in Mathematics, vol.134, issue.1, pp.90-145, 1998.
DOI : 10.1006/aima.1997.1650

G. Geometry and . Group, Non-manifold Meshes Repository, 2009.

R. Ghrist and A. Muhammad, Coverage and hole-detection in sensor networks via homology, IPSN 2005. Fourth International Symposium on Information Processing in Sensor Networks, 2005., 2005.
DOI : 10.1109/IPSN.2005.1440933

M. Giesbrecht, Probabilistic computation of the Smith normal form of a sparse integer matrix, Lecture Notes in Computer Science, vol.1122, pp.173-186, 1996.
DOI : 10.1007/3-540-61581-4_53

R. González-díaz, M. J. Jiménez, B. Medrano, and P. Real, Chain homotopies for object topological representations, Discrete Applied Mathematics, vol.157, issue.3, pp.490-499, 2009.
DOI : 10.1016/j.dam.2008.05.029

C. Gotsman, K. Kaligosi, K. Mehlhorn, D. Michail, and E. Pyrga, Cycle bases of graphs and sampled manifolds, Computer Aided Geometric Design, vol.24, issue.8-9, pp.464-480, 2007.
DOI : 10.1016/j.cagd.2006.07.001

J. L. Hafner and K. S. Mccurley, Asymptotically Fast Triangularization of Matrices over Rings, SIAM Journal on Computing, vol.20, issue.6, pp.1068-1083, 1991.
DOI : 10.1137/0220067

A. Hatcher, Algebraic Topology. Cambr, 2002.

A. Hui and L. De-floriani, A two-level topological decomposition for non-manifold simplicial shapes, Proceedings of the 2007 ACM symposium on Solid and physical modeling , SPM '07, pp.355-260, 2007.
DOI : 10.1145/1236246.1236297

T. Kaczynski, M. Mrozek, and M. Slusarek, Homology computation by reduction of chain complexes, Computers & Mathematics with Applications, vol.35, issue.4, pp.35-39, 1998.
DOI : 10.1016/S0898-1221(97)00289-7

R. Kannan, A. , and B. , Polynomial Algorithms for Computing the Smith and Hermite Normal Forms of an Integer Matrix, SIAM Journal on Computing, vol.8, issue.4, pp.499-507, 1979.
DOI : 10.1137/0208040

M. Mrozek, P. Pilarczyk, and N. Zelazna, Homology algorithm based on acyclic subspace, Computers & Mathematics with Applications, vol.55, issue.11, pp.2395-2412, 2008.
DOI : 10.1016/j.camwa.2007.08.044

J. Munkres, Algebraic Topology, 1999.

S. Peltier, A. Ion, W. G. Kropatsch, G. Damiand, and Y. Haxhimusa, Directly computing the generators of image homology using graph pyramids, Image and Vision Computing, vol.27, issue.7, pp.846-853, 2009.
DOI : 10.1016/j.imavis.2008.06.009
URL : https://hal.archives-ouvertes.fr/hal-00366086

F. Sergeraert, The Computability Problem in Algebraic Topology, Advances in Mathematics, vol.104, issue.1, pp.139-155, 1994.
DOI : 10.1006/aima.1994.1018

F. Sergeraert, Constructive algebraic topology, ACM SIGSAM Bulletin, vol.33, issue.3, pp.13-25, 1999.
DOI : 10.1145/347127.347138
URL : https://hal.archives-ouvertes.fr/hal-00126384

F. Sergeraert and J. Rubio, Constructive homological algebra and applications, 2006.

A. Storjohann, Near optimal algorithms for computing Smith normal forms of integer matrices, Proceedings of the 1996 international symposium on Symbolic and algebraic computation , ISSAC '96, pp.267-274, 1996.
DOI : 10.1145/236869.237084

A. Thakur, A. G. Banerjee, and S. K. Gupta, A survey of CAD model simplification techniques for physics-based simulation applications, Computer-Aided Design, vol.41, issue.2, pp.65-80, 2009.
DOI : 10.1016/j.cad.2008.11.009

X. Zhu, R. Sarkar, and J. Gao, Topological Data Processing for Distributed Sensor Networks with Morse-Smale Decomposition, IEEE INFOCOM 2009, The 28th Conference on Computer Communications, pp.2911-2915, 2009.
DOI : 10.1109/INFCOM.2009.5062257

A. Zomorodian and G. Carlsson, Localized homology, Computational Geometry, vol.41, issue.3, pp.126-148, 2008.
DOI : 10.1016/j.comgeo.2008.02.003
URL : http://doi.org/10.1016/j.comgeo.2008.02.003