Homological properties of periodic homeomorphisms of 4-manifolds
type: Item
instance of: scholarly article
title: Homological properties of periodic homeomorphisms of 4-manifolds
zbMATH Open document ID: 0667.57024
DOI: 10.1215/S0012-7094-89-05812-2
author: Reinhard Schultz
author: Slawomir Kwasik
published in: Duke Mathematical Journal
publication date: 1989-01-01T00:00:00Z
review text: This paper shows that certain homological results are valid for periodic homeomorphisms of four dimensional manifolds even though they are not more generally. The first example is: Theorem. If f: \(M^ 4\to M^ 4\) is a periodic homeomorphism of a closed four dimensional manifold, then the Lefschetz number of f is the Euler characteristic of the fixed point set of f. The other examples given concern the ideal class invariant \(\alpha\) (M,f)\(\in \tilde K_ 0(Z[Z_ p])\) for a homeomorphism f of odd prime period p on a closed simply connected four manifold. The results say that \(\alpha (M,f)=0\) if f is locally linear, and more generally \(\alpha\) (M,f) can be any invariant of the canonical conjugation.
Mathematics Subject Classification ID: 57S17
Mathematics Subject Classification ID: 55M20
zbMATH DE Number: 4092371
zbMATH Keywords: periodic homeomorphisms of four dimensional manifolds
zbMATH Keywords: Lefschetz number
zbMATH Keywords: Euler characteristic of the fixed point set
zbMATH Keywords: ideal class invariant
MaRDI profile type: Publication
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full work available at URL: s0012-7094-89-05812-2
OpenAlex ID: W2013335670
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description: scientific article; zbMATH DE number 4092371