Algebraic and Geometric Topology 4 (2004), paper no. 13, pages 219-241.

Adem relations in the Dyer-Lashof algebra and modular invariants

Nondas E. Kechagias

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.

Keywords. Adem relations, Dyer-Lashof algebra, Dickson algebra, Borel invariants

AMS subject classification. Primary: 55S10, 13F20. Secondary: 55P10.

DOI: 10.2140/agt.2004.4.219

E-print: arXiv:math.AT/0404411

Submitted: 23 October 2003. (Revised: 20 January 2004.) Accepted: 23 January 2004. Published: 13 April 2004.

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Nondas E. Kechagias
Department of Mathematics, University of Ioannina, 45110 Greece

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