Adem relations in the Dyer–Lashof algebra and modular invariants

Kechagias, Nondas E

doi:10.2140/agt.2004.4.219

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Adem relations in the Dyer–Lashof algebra and modular invariants

Nondas E Kechagias

Algebraic & Geometric Topology 4 (2004) 219–241

DOI: 10.2140/agt.2004.4.219

arXiv: math.AT/0404411

Abstract

This work deals with Adem relations in the Dyer–Lashof algebra from a modular invariant point of view. The main result is to provide an algorithm which has two effects: Firstly, to calculate the hom-dual of an element in the Dyer–Lashof algebra; and secondly, to find the image of a non-admissible element after applying Adem relations. The advantage of our method is that one has to deal with polynomials instead of homology operations. A moderate explanation of the complexity of Adem relations is given.

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Keywords

Adem relations, Dyer–Lashof algebra, Dickson algebra, Borel invariants

Mathematical Subject Classification 2000

Primary: 55S10, 13F20

Secondary: 55P10

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Publication

Received: 23 October 2003

Revised: 20 January 2004

Accepted: 23 January 2004

Published: 13 April 2004

Corrected: 9 January 2009 (link on page 221 updated)

Authors

Nondas E Kechagias
Department of Mathematics University of Ioannina 45110 Greece
http://www.math.uoi.gr/~nondas_k

Volume 4, issue 1 (2004)