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On Formulae of Thom and Wu
Author(s) -
Adams J. F.
Publication year - 1961
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/s3-11.1.741
Subject(s) - citation , mathematics , combinatorics , algebra over a field , library science , computer science , pure mathematics
1. RECENTLY, in preparing a set of lectures on characteristic classes, I had occasion to consider the formulae of Thorn and Wu (10) which relate Stiefel-Whitney classes to Steenrod squares. Briefly, they are as follows. Let M be a compact differentiate w-manifold, not necsssarily orientable, with fundamental class n e Hn(M; Z2). Then there is a unique class VteH'iM; Z2) such that (Sq'x, fx} = (vtx, fx} for each x e H"-'(M; Z2); and the Stiefel-Whitney classes wk e H (M; Z2) satisfy «•» = I
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