Previous |  Up |  Next


twisted product; reduction; chain complex
In the paper weak sufficient conditions for the reduction of the chain complex of a twisted cartesian product $F \times _{\tau }B$ to a chain complex of free finitely generated abelian groups are found.
[1] Čadek, M., Krčál, M., Matoušek, J., Sergeraert, F., Vokřínek, L., Wagner, U.: Algorithmic solvability of lifting extension problem. in preparation.
[2] Čadek, M., Krčál, M., Matoušek, J., Sergeraert, F., Vokřínek, L., Wagner, U.: Computing all maps into a sphere. Proceedings of the Twenty-Third Annual ACM-SIAM Symposium on Discrete Algorithms, 2012.
[3] Eilenberg, S., MacLane, S.: On the group $H(\Pi , n)$, I. Ann. of Math. (2) 58 (1953), 55–106.
[4] Krčál, M., Matoušek, J., Sergeraert, F.: Polynomial–time homology for simplicial Eilenberg–MacLane spaces. arXiv:1201.6222v1 (2012).
[5] Lambe, L., Stasheff, J.: Applications of perturbation theory to iterated fibrations. Manuscripta Math. 58 (1987), 363–376. DOI 10.1007/BF01165893 | MR 0893160 | Zbl 0632.55011
[6] May, J. P.: Simplicial objects in algebraic topology Chicago Lectures in Mathematics. Chicago Lectures in Mathematics, University of Chicago Press, Chicago, IL, 1992, Reprint of the 1967 original. MR 1206474
[7] Romero, A., Sergeraert, F.: Discrete vector fields and fundamental algebraic topology. arXiv:1005.5685v1 (2010).
[8] Rubio, J.: Homologie effective des espaces de lacets itérés: un logiciel. Ph.D. thesis, Institut Fourier, Grenoble, 1991.
[9] Rubio, J., Sergeraert, F.: Constructive homological algebra and applications. Genova Summer School 2006, arXiv:1208.3816v2.
[10] Weishu, Shih: Homologie des espaces fibrés. Publ. Math., Inst. Hautes Étud. Sci. 13 (1962), 93–176. MR 0144348
Partner of
EuDML logo