Thom modules and pseudoreflection groups
type: Item
instance of: scholarly article
title: Thom modules and pseudoreflection groups
zbMATH Open document ID: 0683.55012
DOI: 10.1016/0022-4049(89)90104-7
author: Larry Smith
author: Carles Broto
author: R. E. Stong
published in: Journal of Pure and Applied Algebra
publication date: 1989-01-01T00:00:00Z
review text: Let \(R^*\) be an unstable algebra over the mod p Steenrod algebra \({\mathcal A}^*\). A Thom module over \(R^*\) is defined to be an \(R^*\)-module M which is free of rank 1 and has a compatible \({\mathcal A}^*\)-action. In particular, the cohomology of the Thom space of an oriented vector bundle is a Thom module over the cohomology of the base space. In analogy with work of \textit{R. Stanley} [J. Algebra 49, 134-148 (1977; Zbl 0383.20029)], the authors construct a Thom module associated to a linear character of a subgroup of \(GL_ n({\mathbb{F}}_ p)\) generated by pseudoreflections. They also give a criterion involving Pontryagin classes for such Thom modules to come from vector bundles.
Mathematics Subject Classification ID: 55R40
Mathematics Subject Classification ID: 55R25
zbMATH DE Number: 4119242
zbMATH Keywords: unstable algebra over the mod p Steenrod algebra
zbMATH Keywords: Thom module
zbMATH Keywords: Thom space
zbMATH Keywords: Pontryagin classes
zbMATH Keywords: vector bundles
MaRDI profile type: Publication
full work available at URL: 0022-4049(89)90104-7
OpenAlex ID: W2039173519
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description: scientific article; zbMATH DE number 4119242