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.

Notes on file formats

Nondas E. Kechagias
Department of Mathematics, University of Ioannina, 45110 Greece
Email: nkechag@cc.uoi.gr
URL: http://www.uoi.gr/schools/scmath/math/staff/nkechag/nkech.htm

AGT home page

EMIS/ELibM Electronic Journals

Outdated Archival Version

These pages are not updated anymore. They reflect the state of 21 Apr 2006. For the current production of this journal, please refer to http://msp.warwick.ac.uk/.