On the homomorphism between the equivariant SK ring and the Burnside ring for involution
type: Item
instance of: scholarly article
title: On the homomorphism between the equivariant SK ring and the Burnside ring for involution
zbMATH Open document ID: 0591.57015
author: Hiroaki Koshikawa
published in: Hokkaido Mathematical Journal
publication date: 1985-01-01T00:00:00Z
review text: Let G be a finite Abelian group. If M and N are smooth G-manifolds, then say \(M\sim N\) if the H-fixed point sets \(M^ H\) and \(N^ H\) have the same Euler characteristics for all \(H\leq G\). The Burnside ring A(G) of G is realized as equivalence classes [M] with sum corresponding to disjoint union and product to Cartesian product. Let \(SK_*^ G\) denote the G- equivariant ''cutting and pasting'' ring formed from smooth G-manifolds M; there is a natural ring homomorphism \(\phi\) : SK\({}^ G_*\to A(G)\). Set \(SK_*=SK_*^{(1)}\); then \(SK^ G_*\) is an \(SK_*\)-algebra. In this paper, the \(SK_*\)-algebra structure of \(SK_*^{Z_ 2}\) is determined explicitly as well as the kernel of the homomorphism \(\phi\) into \(A(Z_ 2)\).
Mathematics Subject Classification ID: 57S17
Mathematics Subject Classification ID: 57R85
zbMATH DE Number: 3949321
zbMATH Keywords: equivariant cutting and pasting ring
zbMATH Keywords: finite Abelian group
zbMATH Keywords: smooth G- manifolds
zbMATH Keywords: fixed point sets
zbMATH Keywords: Euler characteristics
zbMATH Keywords: Burnside ring
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.14492/hokmj/1381757661
OpenAlex ID: W2075149584
DOI: 10.14492/HOKMJ/1381757661
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description: scientific article; zbMATH DE number 3949321