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Self-intersection of fixed manifolds and relations for the multisignature. (English) Zbl 0768.57018

Let on a smooth, orientable \(2n\)-manifold \(M\) be given a closed orientable \((2n-2)\)-submanifold \(K_ x\), which is dual to a cohomology class \(x\in H^ 2(M;\mathbb{Z})\). Let \(K^{(s)}_ x\) denote the \(s\)-fold self-intersection of \(K_ x\) in \(M\). The first result in the paper expresses the signature of \(K^{(s)}_{dx}\) in terms of the signature of \(K^{(s)}_ x\), where \(d\) is a non-negative integer. This result is applied to the study of finite group actions on the manifold \(M\) which fix a codimension 2 submanifold \(F\). Namely, the author specifies the contribution of \(F\) in a multisignature problem.
Reviewer: D.Motreanu (Iaşi)

MSC:

57S17 Finite transformation groups
57R20 Characteristic classes and numbers in differential topology
57R19 Algebraic topology on manifolds and differential topology
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