Algebraic & Geometric Topology

Adem relations in the Dyer–Lashof algebra and modular invariants

Nondas E Kechagias

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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.

Article information

Algebr. Geom. Topol., Volume 4, Number 1 (2004), 219-241.

Received: 23 October 2003
Revised: 20 January 2004
Accepted: 23 January 2004
First available in Project Euclid: 21 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 55S10: Steenrod algebra 13F20: Polynomial rings and ideals; rings of integer-valued polynomials [See also 11C08, 13B25]
Secondary: 55P10: Homotopy equivalences

Adem relations Dyer–Lashof algebra Dickson algebra Borel invariants


Kechagias, Nondas E. Adem relations in the Dyer–Lashof algebra and modular invariants. Algebr. Geom. Topol. 4 (2004), no. 1, 219--241. doi:10.2140/agt.2004.4.219.

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