Homotopy types of locally linear representation forms
type: Item
instance of: scholarly article
title: Homotopy types of locally linear representation forms
zbMATH Open document ID: 0871.57038
DOI: 10.1007/BF02567803
published in: Manuscripta Mathematica
publication date: 1997-09-23T00:00:00Z
full work available at URL: https://eudml.org/doc/156108
review text: \textit{I. Madsen} and \textit{M. Raussen} [Osaka J. Math 27, 567-591 (1990; Zbl 0715.57019)] investigated certain locally linear actions of a cyclic group of odd order on homotopy spheres, the so-called \(G\)-representation form. In particular, several conditions on a dimension function were described that made sure that it can be realized as the dimension function of a \(G\)-representation form. It remained unclear, whether all homotopy types with those dimension functions would support a locally linear structure. It is the aim of this note to show that this is not always the case.
Mathematics Subject Classification ID: 57S25
Mathematics Subject Classification ID: 57S17
Mathematics Subject Classification ID: 20C99
zbMATH DE Number: 866148
zbMATH Keywords: equivariant splitting
zbMATH Keywords: restriction homomorphism
zbMATH Keywords: representation form
zbMATH Keywords: homotopy spheres
zbMATH Keywords: dimension function
author: Erkki Laitinen
author: Martin Raussen
reviewed by: Saroop K. Kaul
MaRDI profile type: Publication
cites work: Q3050437
cites work: A geometric algebraicity property for moduli spaces of compact Kähler manifolds with \(h^{2,0}=1\)
cites work: Representation forms for metacyclic groups
cites work: Q3732573
cites work: Locally linear representation forms
cites work: On the classification of G-spheres. I. Equivariant transversality
cites work: Homotopy representations and spheres of representations
cites work: Linearity of homotopy representations
cites work: Linearity of homotopy representations. II
cites work: Q3901698
cites work: Transformation groups and representation theory
cites work: Transformation groups
cites work: Q4039935
cites work: Homotopy representations of finite groups
cites work: Classification of Hermitian forms. VI: Group rings
OpenAlex ID: W2026336612
description: scientific article; zbMATH DE number 866148