Adem relations in the Dyer-Lashof algebra and modular invariants

Mathematics – Algebraic Topology

Scientific paper

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Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol4/agt-4-13.abs.html

Scientific paper

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.

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