Involutions fixing the disjoint union of 3-real projective space with Dold manifold
type: Item
instance of: scholarly article
title: Involutions fixing the disjoint union of 3-real projective space with Dold manifold
zbMATH Open document ID: 0964.57032
author: Zhi Lü
author: Xibo Liu
published in: Kodai Mathematical Journal
publication date: 2001-03-12T00:00:00Z
review text: This paper determines the cobordism classification of smooth involutions \((M,T)\) having fixed point set the union of the projective space \(\mathbb{R} P^3\) and a Dold manifold \(P(m,n)\). It is assumed that the normal bundle of \(\mathbb{R} P^3\) in \(M\) does not bound and that \(m\) and \(n\) are positive, so that the fixed set is genuinely such a union. The main results are that one must have \(m=3\) and \(n\) even. For each of the possible choices of the normal bundle of \(\mathbb{R} P^3\) there is exactly one possible stable normal bundle for \(P(3,n)\), and the range of dimensions for \(M\) is determined.
Mathematics Subject Classification ID: 57R85
Mathematics Subject Classification ID: 57R90
Mathematics Subject Classification ID: 55N22
zbMATH DE Number: 1547124
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2996/kmj/1138044210
OpenAlex ID: W1991155588
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DOI: 10.2996/KMJ/1138044210
description: scientific article; zbMATH DE number 1547124