Rigid versus non-rigid cyclic actions
type: Item
instance of: scholarly article
title: Rigid versus non-rigid cyclic actions
zbMATH Open document ID: 0694.57025
DOI: 10.1007/BF02564675
author: Mikiya Masuda
author: Dong Youp Suh
author: Karl Heinz Dovermann
published in: Commentarii Mathematici Helvetici
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/140154
review text: The authors study locally smooth \({\mathbb{Z}}_ p\)-actions (p odd prime) on homotopy \({\mathbb{C}}P^ n\)'s with fixed point-set a codimension two component and an isolated point (Type \(II_ 0)\). They treat the question of algebraic standardness as introduced by \textit{K. H. Dovermann} [Math. Proc. Camb. Philos. Soc. 101, 487-507 (1987; Zbl 0629.57025)]. Theorem A: Let X be a cohomology \({\mathbb{C}}P^ n\). Then there is a constant \(c_ x\), which depends only on the Pontryagin class of X, such that any locally smooth \({\mathbb{Z}}_ p\) action of Type \(II_ 0\) is algebraically standard if \(p\geq c_ x.\) If \(n\gg 2p\) they in contrast obtain also that there are infinitely many homotopy \({\mathbb{C}}P^ n\)'s of Type \(II_ 0\) with nonstandard Pontryagin class (Theorem B). They conjecture: There exists a function d(n) such that Type \(II_ 0\) actions on cohomology \({\mathbb{C}}P^ n\)'s are algebraically standard if \(p\geq d(n)\). The proofs make use of careful estimates of terms supplied by the G-signature theorem and surgery-theory.
Mathematics Subject Classification ID: 57S25
Mathematics Subject Classification ID: 57S17
Mathematics Subject Classification ID: 57R67
Mathematics Subject Classification ID: 58J20
zbMATH DE Number: 4137030
zbMATH Keywords: locally smooth \({\mathbb{Z}}_ p\)-actions on homotopy \({\mathbb{C}}P^ n\prime s\)
zbMATH Keywords: algebraic standardness
zbMATH Keywords: Pontryagin class
zbMATH Keywords: G-signature theorem
zbMATH Keywords: surgery-theory
MaRDI profile type: Publication
OpenAlex ID: W2048023504
description: scientific article; zbMATH DE number 4137030