Free involutions on \(S ^{2} \times S ^{3}\)
type: Item
instance of: scholarly article
title: Free involutions on \(S ^{2} \times S ^{3}\)
zbMATH Open document ID: 1246.57078
author: Yang Su
published in: Geometriae Dedicata
publication date: 2012-07-31T00:00:00Z
full work available at URL: https://arxiv.org/abs/0907.2800
review text: Free involutions are the simplest type of symmetries that a smooth manifold can admit and their classification is an old problem in transformation groups. The classification of free involutions on a simply-connected manifold up to conjugation is equivalent to the classification of their orbit spaces. In the paper under review, the author gives a classification of smooth 5-manifolds with fundamental group \(\mathbb{Z}/2\) and universal cover \(\mathbb{S}^2 \times \mathbb{S}^3\). As a consequence, he obtains the classification of smooth free involutions on \(\mathbb{S}^2 \times \mathbb{S}^3\) up to conjugation. The author also gives explicit examples of free involutions on \(\mathbb{S}^2 \times \mathbb{S}^3\).
reviewed by: Mahender Singh
Mathematics Subject Classification ID: 57R67
Mathematics Subject Classification ID: 57R75
Mathematics Subject Classification ID: 57S99
zbMATH DE Number: 6062591
zbMATH Keywords: bordism
zbMATH Keywords: free involutions
zbMATH Keywords: surgery
MaRDI profile type: Publication
OpenAlex ID: W2059638365
arXiv ID: 0907.2800
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DOI: 10.1007/S10711-011-9642-8
description: scientific article; zbMATH DE number 6062591