On Wall manifolds with (\(\epsilon\) )-free involutions
type: Item
instance of: scholarly article
title: On Wall manifolds with (\(\epsilon\) )-free involutions
zbMATH Open document ID: 0622.57023
author: Tamio Hara
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 1986-01-01T00:00:00Z
review text: Wall manifolds are manifolds M with a classifying map \(\alpha: M\to {\mathbb{R}}P^{\infty}\), with \(\alpha(M)\subset {\mathbb{R}}P^ 1\), for the determinant line bundle det \(\tau_ M\) of the tangent bundle \(\tau_ M\). Let \(W_*\) be the bordism ring of Wall manifolds, and \(W_*^+({\mathbb{Z}}_ 2)\) (resp. \(W_*^-({\mathbb{Z}}_ 2))\) be the bordism group of Wall manifolds M with fixed point free involution \(\mu\) with \({\tilde \alpha}\circ \det d\mu ={\tilde \alpha}\) (resp. \({\tilde \alpha}\circ \det d\mu =-{\tilde \alpha})\), where \({\tilde \alpha}\) is a bundle map of det \(\tau_ M\) which covers \(\alpha\) and \(d\mu\) is the differential of \(\mu\). The paper under review explicitly presents bases of \(W^+_*({\mathbb{Z}}_ 2)\) and \(W^-_*({\mathbb{Z}}_ 2)\) as \(W_*\)- modules. It also presents bases of their images in the unoriented bordism group of fixed point free involutions.
Mathematics Subject Classification ID: 57R85
Mathematics Subject Classification ID: 57R15
Mathematics Subject Classification ID: 57S17
zbMATH DE Number: 4009350
zbMATH Keywords: bordism group of Wall manifolds with fixed point free involution
zbMATH Keywords: determinant line bundle
zbMATH Keywords: unoriented bordism group of fixed point free involutions
reviewed by: Katsuhiro Komiya
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1195177854
OpenAlex ID: W2256658303
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DOI: 10.2977/PRIMS/1195177854
description: scientific article; zbMATH DE number 4009350