Stable systolic category of the product of spheres

Ryu, Hoil

doi:10.2140/agt.2011.11.983

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Stable systolic category of the product of spheres

Hoil Ryu

Algebraic & Geometric Topology 11 (2011) 983–999

DOI: 10.2140/agt.2011.11.983

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

References

Publication

Received: 17 July 2010

Revised: 27 October 2010

Accepted: 23 December 2010

Published: 25 March 2011

Authors

Hoil Ryu
Graduate School of Mathematics Kyushu University 774 Motooka Nishi-ku Fukuoka 819-0395 Japan

Volume 11, issue 2 (2011)