Equivariant surgery theory: Construction of equivariant normal maps
type: Item
instance of: scholarly article
title: Equivariant surgery theory: Construction of equivariant normal maps
zbMATH Open document ID: 0827.57014
author: Masaharu Morimoto
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 1995-12-18T00:00:00Z
review text: Following an idea and a description of T. Petrie, many authors have constructed exotic smooth group actions using equivariant surgery. This involves the construction of suitable \(G\)-normal maps via \(G\)- transversality, and an arrangement that makes \(G\)-surgery obstructions vanish. It is difficult to find detailed and uptodate statements and proofs concerning the construction of \(G\)-normal maps in the literature. This paper is devoted to those details and their proofs (e.g., for Petrie's transversality theorem) involving steps of both a combinatorial (Burnside ring) and a topological nature. Moreover, it contains nice results about localization in Burnside rings that are essential for the results about smooth one-fixed-point actions of Oliver groups on spheres due to the author, E. Laitinen and K. Pawałowski.
Mathematics Subject Classification ID: 57R65
Mathematics Subject Classification ID: 57R85
Mathematics Subject Classification ID: 57R91
zbMATH DE Number: 785371
zbMATH Keywords: equivariant transversality
zbMATH Keywords: equivariant normal map
zbMATH Keywords: Petrie's transversality theorem
zbMATH Keywords: localization
zbMATH Keywords: Burnside rings
zbMATH Keywords: Oliver groups
reviewed by: Martin Raussen
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1195164796
OpenAlex ID: W2026661123
cites work: Q4872057
cites work: Transformation groups and representation theory
cites work: A characterisation of solvable groups
cites work: Equivariant L-theory. I
cites work: Finite groups with smooth one fixed point actions on spheres
cites work: On one fixed point actions on spheres
cites work: Q3468325
cites work: Most standard spheres have smooth one fixed point actions of \(A_ 5\). II
cites work: Q3975389
cites work: Fixed-point sets of group actions on finite acyclic complexes
cites work: Q4195625
cites work: One fixed point actions on spheres. I,II
cites work: Q3694282
DOI: 10.2977/PRIMS/1195164796
description: scientific article; zbMATH DE number 785371