#### 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

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