Cohomological dimension, self-linking, and systolic geometry

Autor:	Dranishnikov, Alexander N., Katz, Mikhail G., Rudyak, Yuli B.
Rok vydání:	2008
Předmět:	Mathematics - Differential Geometry Mathematics - Algebraic Topology 53C23 55M30 57N65
Druh dokumentu:	Working Paper
Popis:	Given a closed manifold M, we prove the upper bound of (n+d)/2 for the length of a product of systoles that can form a curvature-free lower bound for the total volume of M, in the spirit of M. Gromov's systolic inequalities. Here n is the dimension of M, while d is the is the cohomological dimension of its fundamental group. We apply this upper bound to show that, in the case of a 4-manifold, the Lusternik--Schnirelmann category is an upper bound for such length. Furthermore we prove a systolic inequality on a manifold M with b_1(M)=2 in the presence of a nontrivial self-linking class of the typical fiber of its Abel--Jacobi map to the 2-torus. Comment: 15 pages; to appear in Israel Journal of Mathematics
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/0807.5040 Zobrazit plný text záznamu View this record from Arxiv