Circle actions on Kähler spaces
type: Item
instance of: scholarly article
title: Circle actions on Kähler spaces
zbMATH Open document ID: 0809.57021
DOI: 10.1016/0022-4049(94)90133-3
author: Christopher Allday
published in: Journal of Pure and Applied Algebra
publication date: 1994-03-01T00:00:00Z
review text: The author studies an old problem in cohomology theory of transformation groups: ``If \(G = S^ 1\) or \(G = Z/p\) is acting on a Kähler manifold \(M\) with the fixed point set \(M^ G \neq \emptyset\), then each component of \(M^ G\) must resemble a Kähler manifold cohomologically'' [\textit{W. Browder}, Topology 27, No. 4, 459-472 (1988; Zbl 0669.57023)]. He gives an answer to this problem with an example of a semi-free circle group action on a cohomology Kähler manifold such that no component of the fixed point set is a cohomology Kähler manifold.
Mathematics Subject Classification ID: 57S15
Mathematics Subject Classification ID: 57S17
Mathematics Subject Classification ID: 57S25
zbMATH DE Number: 500563
zbMATH Keywords: Kähler manifold
zbMATH Keywords: fixed point set
zbMATH Keywords: semi-free circle group action
zbMATH Keywords: cohomology Kähler manifold
MaRDI profile type: Publication
full work available at URL: 0022-4049(94)90133-3
OpenAlex ID: W2016803165
cites work: Q5658847
cites work: Actions of elementary Abelian p-groups
cites work: Real homotopy theory of Kähler manifolds
cites work: Q3810543
cites work: DGA homology decompositions and a condition for formality
cites work: Deformations of algebras and cohomology of fixed point sets
description: scientific article; zbMATH DE number 500563