Geometric realization of Adams maps
type: Item
instance of: scholarly article
title: Geometric realization of Adams maps
zbMATH Open document ID: 1220.55010
author: Xianzu Lin
publication date: 2011-06-24T00:00:00Z
review text: This paper considers certain maps on the rational cohomology rings of homogeneous spaces and asks when they are realized by a map of the underlying space. Let \(G\) be a compact, connected Lie group, \(P\) a connected subgroup of equal rank, and let \(l_k\) be the Adams map on \(H^*(G/P;{\mathbb Q})\) which, in degree \(2i\), is multiplication by the integer \(k^i\). It is shown that if \(k\) is prime to the order of the Weyl group of \(G\), then \(l_k\) can be realized by a continuous function. Some examples of non-realizability are given in cases where this coprimality hypothesis does not hold.
reviewed by: Martin D. Crossley
Mathematics Subject Classification ID: 55S37
Mathematics Subject Classification ID: 57T15
zbMATH DE Number: 5912902
zbMATH Keywords: homogeneous space
zbMATH Keywords: self map
zbMATH Keywords: Adams map
zbMATH Keywords: Lie group
MaRDI profile type: Publication
full work available at URL: s10114-011-0164-y
OpenAlex ID: W2095658874
DOI: 10.1007/S10114-011-0164-Y
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 5912902