Cohomological dimension, self-linking, and systolic geometry

Alexander N. Dranishnikov, Mikhail G. Katz, Yuli B. Rudyak

Research output: Contribution to journalArticlepeer-review

Abstract

Given a closed manifold M, we prove the upper bound of 1/2(dim M + cdπ1M)) for the number of systolic factors in a curvature-free lower bound for the total volume of M, in the spirit of M. Gromov's systolic inequalities. Here "cd" is the cohomological dimension. We apply this upper bound to show that, in the case of a 4-manifold, the Lusternik-Schnirelmann category is an upper bound for the systolic category. Furthermore, we prove a systolic inequality on a manifold M with b1(M) = 2 in the presence of a nontrivial self-linking class of a typical fiber of its Abel-Jacobi map to the 2-torus.

Original languageEnglish
Pages (from-to)437-453
Number of pages17
JournalIsrael Journal of Mathematics
Volume184
Issue number1
DOIs
StatePublished - Aug 2011

All Science Journal Classification (ASJC) codes

  • General Mathematics

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