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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Adem relations in the Dyer–Lashof algebra and modular invariants

Nondas E Kechagias

Algebraic & Geometric Topology 4 (2004) 219–241

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.

Additional material
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