Note on the rational cohomology of the function space of based maps
type: Item
instance of: scholarly article
title: Note on the rational cohomology of the function space of based maps
zbMATH Open document ID: 1065.55005
author: Yasusuke Kotani
published in: Homology, Homotopy and Applications
publication date: 2005-04-05T00:00:00Z
full work available at URL: https://eudml.org/doc/51414
full work available at URL: volume6-1.htm
review text: Let \(\text{map}_*(X,Y)\) be the space of based maps from \(X\) to \(Y\). Assume that \(X\) is a \(\mathbb{Q}\)-formal path connected finite CW-complex and \(Y\) is a \(r\)-connected space with \(r\geq\dim X\). The author uses the Haefliger model for a space of maps [\textit{A. Haeflinger}, Trans Am. Math. Soc. 273, 609--620 (1982; Zbl 0508.55019)] in order to determine the necessary and sufficient conditions for the rational algebra \(H^*(\text{map}_*(X,Y); \mathbb{Q})\) to be free.
reviewed by: Jean-Claude Thomas
Mathematics Subject Classification ID: 55P62
zbMATH DE Number: 2153116
zbMATH Keywords: mapping space
zbMATH Keywords: Haefliger model
MaRDI profile type: Publication
DOI: 10.4310/HHA.2004.V6.N1.A18
description: scientific article; zbMATH DE number 2153116