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 language | English |
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Pages (from-to) | 437-453 |
Number of pages | 17 |
Journal | Israel Journal of Mathematics |
Volume | 184 |
Issue number | 1 |
DOIs | |
State | Published - Aug 2011 |
All Science Journal Classification (ASJC) codes
- General Mathematics