Equivariant evaluation on free loop spaces
type: Item
instance of: scholarly article
title: Equivariant evaluation on free loop spaces
zbMATH Open document ID: 0991.55003
author: Iver Ottosen
published in: Mathematische Zeitschrift
publication date: 2002-06-27T00:00:00Z
review text: For each positive integer \(k\), let us consider the evaluation map \(\Lambda X \to X^k\) which sends a loop to its values at the \(k\)-th roots of unity \(\in S^1=\{\alpha\in \mathbb C:|\alpha |=1\}\), where \(\Lambda X\) denotes the free loop space on \(X\). Since this map is equivariant with respect to the action of the cyclic group \(C_k\) of \(k\) elements, the author hopes to study the induced map in \(C_k\)-equivariant cohomology. In particular, in this paper, for \(k=2^m\) with \(m\geq 1\), he computes the map induced by evaluation in \(C_k\)-equivariant cohomology with \(\mathbb Z/2\)-coefficients in terms of the approximation functor \(l\) [\textit{M. Bökstedt} and the author, Fundam. Math. 162, No. 3, 251-275 (1999; Zbl 0952.55006)].
reviewed by: Kohhei Yamaguchi
Mathematics Subject Classification ID: 55N91
Mathematics Subject Classification ID: 55P35
Mathematics Subject Classification ID: 55S15
zbMATH DE Number: 1761113
zbMATH Keywords: evaluation map
zbMATH Keywords: free loop space
zbMATH Keywords: equivariant cohomology
zbMATH Keywords: Steenrod algebra
zbMATH Keywords: approximation functor
zbMATH Keywords: Borel construction
MaRDI profile type: Publication
full work available at URL: s002090100333
OpenAlex ID: W2036544591
DOI: 10.1007/S002090100333
description: scientific article; zbMATH DE number 1761113