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

A. Zomorodian and G. Carlsson, Computing Persistent Homology, Discrete & Computational Geometry, vol.33, issue.2, pp.249-274, 2005.
DOI : 10.1007/s00454-004-1146-y

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.10.5064

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

H. Edelsbrunner and J. Harer, Persistent homology???a survey, Surveys on Discrete and Computational Geometry. Twenty Years, pp.257-282, 2008.
DOI : 10.1090/conm/453/08802

G. Carlsson, V. De, and S. , Zigzag Persistence, Foundations of Computational Mathematics, vol.33, issue.2, pp.367-405, 2010.
DOI : 10.1007/s10208-010-9066-0

G. Carlsson, D. Vin-de-silva, and . Morozov, Zigzag persistent homology and realvalued functions, Proceedings of the Annual Symposium on Computational Geometry, pp.247-256, 2009.

J. R. Munkres, Elements of Algebraic Topology, 1984.

T. Kaczynski, K. Mischaikow, and M. Mrozek, Computational Homology, 2004.
DOI : 10.1007/b97315

R. James, J. E. Bunch, and . Hopcroft, Triangular Factorization and Inversion by Fast Matrix Multiplication, Mathematics of Computation, vol.28, issue.125, pp.231-236, 1974.

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

J. Friedman, Computing Betti numbers via combinatorial Laplacians, STOC '96: Proceedings of the twenty-eighth annual ACM symposium on Theory of computing, pp.386-391, 1996.

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, 2009.
DOI : 10.1007/s10208-008-9027-z

D. Cohen-steiner, H. Edelsbrunner, J. Harer, and D. Morozov, Persistent Homology for Kernels, Images, and Cokernels, SODA '09: Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms, pp.1011-1020, 2009.
DOI : 10.1137/1.9781611973068.110

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

M. Mrozek, N. Pilarczyk, and . 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

T. Lewiner, H. Lopes, and G. Tavares, Optimal discrete Morse functions for 2-manifolds, Computational Geometry, vol.26, issue.3, pp.221-233, 2003.
DOI : 10.1016/S0925-7721(03)00014-2

E. Omer, T. F. Gecio?glugecio?glu, and . Gonzalez, A computationally intractable problem on simplicial complexes, Comput. Geom. Theory Appl, vol.6, issue.2, pp.85-98, 1996.

M. Joswig and M. E. Pfetsch, Computing Optimal Morse Matchings, SIAM Journal on Discrete Mathematics, vol.20, issue.1, pp.11-25, 2006.
DOI : 10.1137/S0895480104445885

A. Zomorodian, The tidy set, Proceedings of the 2010 annual symposium on Computational geometry, SoCG '10, pp.257-266, 2010.
DOI : 10.1145/1810959.1811004

V. Strassen, Gaussian elimination is not optimal, Numerische Mathematik, vol.13, issue.4, pp.354-356, 1969.
DOI : 10.1007/BF02165411

URL : http://www.digizeitschriften.de/download/PPN362160546_0013/PPN362160546_0013___log38.pdf

D. Coppersmith and S. Winograd, Matrix multiplication via arithmetic progressions, Proceedings of the nineteenth annual ACM conference on Theory of computing , STOC '87, pp.251-280, 1990.
DOI : 10.1145/28395.28396

URL : http://doi.org/10.1016/s0747-7171(08)80013-2

H. Cohn, R. Kleinberg, B. Szegedy, and C. Umans, Group-theoretic Algorithms for Matrix Multiplication, 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS'05), pp.379-388, 2005.
DOI : 10.1109/SFCS.2005.39

A. Hatcher, Algebraic Topology INRIA Centre de recherche INRIA Saclay ? Île-de, des Vignes 4, rue Jacques Monod -91893 Orsay Cedex, 2001.