Vol. 31, No. 1, 1969

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ISSN: 0030-8730
Pontryagin squares in the Thom space of a bundle

William Schumacher Massey

Vol. 31 (1969), No. 1, 133–142
Abstract

The object of this note is to determine the action of the Pontryagin squares in the cohomology of the Thom space of a vector bundle. This computation is then applied to the case of the normal bundle of a manifold imbedded in Euclidean space to give simplified proofs of some theorems of Mahowald.

Mathematical Subject Classification
Primary: 57.32
Milestones
Received: 24 February 1969
Published: 1 October 1969
Authors
William Schumacher Massey