Computing betti numbers via combinatorial laplacians

Algorithmica (New York)

Volumn 21, Issue 4, 1998, Pages 331-346

  Friedman, J ^a  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

Betti numbers; Chessboard complexes; Combinatorial laplacian; Power method; Simplicial complexes

Indexed keywords

EID: 0346098118     PISSN: 01784617     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00009218     Document Type: Article

References (19)

1. N. Alon, I. Bárány, Z. Füredi, and D. Kleitman. Point selection and weak ε-nets for convex hulls. Combin. Probab. Comput., 1:189-200, 1992.
2. A. Björner, L. Lovász. S.T. Vrećica, and R.T. Živaljević. Chessboard complexes and matching complexes. J. London Math. Soc., 49:25-39, 1994.
3. I. Chavel. Eigenvalues in Riemannian Geometry. Academic Press, New York, 1984.
4. B. Chazelle. Computational geometry: a retrospective. In D.-Z. Du and F. Hwang, editors, Computing in Euclidean Geometry (2nd edition), pages 22-46. World Scientific Press, Singapore, 1995.
5. J. Dodziuk. Finite-difference approach to the Hodge theory of harmonic forms. Amer. J. Math., 98:79-104, 1976.
6. B.R. Donald and D.R. Chang. On computing the homology type of a triangulation. In Proceedings of the 32nd Annual Symposium on Foundations of Computer Science, pages 650-661, 1991. Also preprint (of the full version).
7. C.J.A. Delfinado and H. Edelsbrunner. An incremental algorithm for Betti numbers of simplicial complexes. In Proceedings of the 9th Annual ACM Conference on Computational Geometry, pages 232-239, 1993.
8. J. Dodziuk and V.K. Patodi. Riemannian structures and triangulations of manifolds. J. Indian Math. Soc., 40:1-52, 1976.
9. B. Eckmann. Harmonische Funktionen und Randvertanfgaben in einem Komplex. Comment. Math. Helv., 17:240-245, 1944-1945.
10. J. Friedman. On the second eigenvalue and random walks in random d-regular graphs. Combinatorica, 11:331-362, 1991.
11. J. Friedman. Probabilistic spaces of Boolean functions of a given complexity: generalities and random k-sat coefficients. July 1992. Preprint.
12. J. Friedman. Minimum higher eigenvalues of Laplacians on graphs. October 1994. To appear in Duke J. Math.
13. J. Friedman. Error bounds on the power method for determining the largest eigenvalue. October 1995. Preprint.
14. J. Friedman and P. Hanlon. On the Betti numbers of chessboard complexes. To appear.
15. P.F. Garst. Some Cohen-Macaulay complexes and group actions. Ph.D. Thesis, University of Madison, WI, 1979.
16. W.V.D. Hodge. The Theory and Applications of Harmonic Integrals. Cambridge University Press, Cambridge, 1941.
17. R. Kannan and A. Bachem. Polynomial algorithms for computing the Smith and Hermite normal forms of an integer matrix. SIAM J. Comput., 8:499-507, 1979.
18. J.R. Munkrees. Elements of Algebraic Topology. Benjamin/Cummings, Redwood City, CA, 1984.
19. R.T. Živaljević and S.T. Vrećica. The colored Tverberg's problem and complexes of injective functions. J. Combin. Theory Ser. A, 61:309-318, 1992.