Computation of cohomology operations on finite simplicial complexes

Homology, Homotopy and Applications

Volumn 5, Issue 2, 2003, Pages 83-93

  Gonzalez Diaz R ^a   Real, P ^a  

^a UNIVERSITY OF SEVILLE   (Spain)

Author keywords

Cohomology operations; Finite simplicial complexes

Indexed keywords

EID: 14744302768     PISSN: 15320073     EISSN: 15320081     Source Type: Journal    
DOI: 10.4310/HHA.2003.v5.n2.a4     Document Type: Conference Paper

References (24)

1. [Ade52] J. Adem. The Iteration of the Steenrod Squares in Algebraic Topology. Proc. Nat. Acad. Sci. USA, v. 38 (1952) 720-724.
2. [Ade58] J. Adem. Operaciones Cohomológicas de Segundo Orden Asociadas a Cuadrados de Steenrod. Symp. Internacional de Topología Algebraica, Univ. of Mexico, Mexico D.F. (1958) 186-221.
3. [DE93] C.J.A. Delfinado, H. Edelsbrunner. An Incremental Algorithm for Betti Numbers of Simplicial Complexes. Proc. 9th Ann. Symp. Comput. Geom. (1993) 232-239.
4. [ELZ00] H. Edelsbrunner, D. Letscher, A. Zomorodian. Topological Persistence and Simplification. Proc. 41st Ann. IEEE Sympos. Found. Comput. Sci. (2000), 454-463.
5. [EM52] S. Eilenberg, S. MacLane. On the Groups of H(Π, n). I. Ann. of Math., v. 58, n. 1 (1952), 55-107.
6. [ES62] N.E. Steenrod, D.B.A. Epstein. Cohomology Operations. Ann. of Math. Studies, v. 50, Princeton University Press, 1962.
7. [For99] R. Forman. Combinatorial Differential Topology and Geometry. New Perspective in Geometric Combinatorics. MSRI Publications, v. 8 (1999) 177-206.
8. [Gon00] R. González-Díaz. Cohomology Operations: A Combinatorial Approach. Ph. D. Thesis, Seville University, May 2000.
9. [GR99] R. González-Díaz, P. Real. A Combinatorial Method for Computing Steenrod Squares. J. of Pure and App. Alg., v. 139 (1999) 89-108.
10. [GL89] V.K.A.M. Gugenheim, L. Lambe. Perturbation Theory in Differential Homological Algebra. I. Illinois J. Math., 33 (1989) 556-582.
11. [GLS91] V.K.A.M. Gugenheim, L. Lambe, J.D. Staheff. Perturbation Theory in Differential Homological Algebra. II. Illinois J. Math., v. 35, n. 3 (1991) 357-373.
12. [GM74] V.K.A.M. Gugenheim, H.J. Munkholm. On the Extended Functoriality of Tor and Color. J. Pure Appl. Algebra, v. 4 (1974) 9-29.
13. ∞-Structures. Bull. Soc. Math. Belg., v. 38 (1986), 237-246.
14. q. The Complex and Symplectic Cases. App. of Algebraic K-Theory to Algebraic Geometry and Number Theory, II. Proc., Boulder, Colorado, 1983. Cont. Math. v. 55 (1986) 487-518.
15. [HK91] J. Huebschmann, T. Kadeishvili. Small Models for Chain Algebras. Math. Z., v. 207 (1991) 245-280.
16. [KMS98] T. Kaczynski, M. Mrozek, M. Slusarek. Homology Computation by Reduction of Chain Complexes. Computers and Mathematics, v. 35, n. 4 (1998) 59-70.
17. [LS87] L. Lambe, J.D. Stasheff. Applications of Perturbation Theory to Iterated Fibrations. Manuscripta Math., v. 58 (1987) 363-376.
18. [McL75] S. MacLane. Homology. Classics in Mathematics, Springer-Verlag, Berlin, 1995. Reprint of the 1975 ed.
19. [Mun76] H.J. Munkholm. The Eilenberg-Moore Spectral Sequence and Strongly Homotopy Multiplicative Maps. J. Pure Appl. Alg., v. 9 (1976) 1-50.
20. [Mun84] J.R. Munkres. Elements of Algebraic Topology. Addison-Wesley Co., 1984.
21. [Rea00] P. Real. Homological Perturbation Theory and Associativity. Homology, Homotopy and its Applications, v. 2, n. 5 (2000) 51-88.
22. [Ser94] F. Sergeraert. The Computability Problem in Algebraic Topology. Adv. Math., v. 104, n. 1 (1994) 1-29.
23. [Ste47] N.E. Steenrod. Products of Cocycles and Exensions of Mappings. Ann. of Math., v. 48 (1947) 290-320.
24. [Tat57] J. Tate. Homology of Noetherian Rings and Locla Rings. Ill. J. of Math., v. 1 (1957) 14-27.