Generators of certain groups of semi-free \(S^ 1\) actions on spheres and splitting of codimension-3 knot exact sequences
type: Item
instance of: scholarly article
title: Generators of certain groups of semi-free \(S^ 1\) actions on spheres and splitting of codimension-3 knot exact sequences
zbMATH Open document ID: 0691.57019
author: Mikiya Masuda
published in: Michigan Mathematical Journal
publication date: 1989-01-01T00:00:00Z
review text: This paper studies the group \(\Sigma^ n_ k(S^ 1)\) of oriented equivariant diffeomorphism classes of smooth semi-free \(S^ 1\) actions on oriented homotopy \((n+2k-1)\)-spheres with fixed set \(S^{n-1}\) having trivial complex normal bundle. The group operation is connected sum. The author defines a homomorphism into the integers if \(n>2k\), and using this shows that Brieskorn spheres with natural actions give either a generator or twice a generator when the group has rank 1.
Mathematics Subject Classification ID: 57S25
Mathematics Subject Classification ID: 57R85
Mathematics Subject Classification ID: 57Q45
zbMATH DE Number: 4131287
zbMATH Keywords: oriented equivariant diffeomorphism classes of smooth semi-free \(S^ 1\) actions on oriented homotopy \((n+2k-1)\)-spheres with fixed set \(S^{n- 1}\)
zbMATH Keywords: Brieskorn spheres
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1307/mmj/1029004007
OpenAlex ID: W1994372106
DOI: 10.1307/MMJ/1029004007
description: scientific article; zbMATH DE number 4131287