Equivariant maps between sphere bundles over tori and KO-degree
Geometric Topology
2007-05-23 v2 Differential Geometry
Abstract
We show a non-existence result for some class of equivariant maps between sphere bundles over tori. The notion of equivariant KO-degree is used in the proof. As an application to Seiberg-Witten theory, for a connected closed oriented spin 4-manifold with indefinite intersection form, we have a new bound of the second Betti number by the signature and a non-negative integer determined by the quadruple cup product on the first cohomology group and some maps in KO-theory induced from the Albanese map.
Cite
@article{arxiv.math/0502511,
title = {Equivariant maps between sphere bundles over tori and KO-degree},
author = {M. Furuta and Y. Kametani},
journal= {arXiv preprint arXiv:math/0502511},
year = {2007}
}
Comments
33 pages, rearranged and partially rewritten