## Abstract

Given a closed manifold M, we prove the upper bound of 1/2(dim M + cdπ_{1}M)) 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 b_{1}(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 |
---|---|

Pages (from-to) | 437-453 |

Number of pages | 17 |

Journal | Israel Journal of Mathematics |

Volume | 184 |

Issue number | 1 |

DOIs | |

State | Published - Aug 2011 |

### Bibliographical note

Funding Information:∗ Supported by the NSF, grant DMS-0604494. ∗∗ Supported by the Israel Science Foundation (grants 84/03 and 1294/06) and the BSF (grant 2006393). † Supported by the NSF, grant 0406311. Received May 26, 2009 and in revised form October 11, 2009

### Funding

∗ Supported by the NSF, grant DMS-0604494. ∗∗ Supported by the Israel Science Foundation (grants 84/03 and 1294/06) and the BSF (grant 2006393). † Supported by the NSF, grant 0406311. Received May 26, 2009 and in revised form October 11, 2009

Funders | Funder number |
---|---|

National Science Foundation | DMS-0604494 |

Bonfils-Stanton Foundation | 2006393, 0406311 |

Israel Science Foundation | 1294/06, 84/03 |