Volume 11, issue 2 (2011)

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Stable systolic category of the product of spheres

Hoil Ryu

Algebraic & Geometric Topology 11 (2011) 983–999
Abstract

The stable systolic category of a closed manifold $M$ indicates the complexity in the sense of volume. This is a homotopy invariant, even though it is defined by some relations between homological volumes on $M$. We show an equality of the stable systolic category and the real cup-length for the product of arbitrary finite dimensional real homology spheres. Also we prove the invariance of the stable systolic category under the rational equivalences for orientable $0$–universal manifolds.

Keywords
cup-length, systoles, stable systolic category
Mathematical Subject Classification 2000
Primary: 57N65
Secondary: 53C23, 55M30