The String Topology Loop Coproduct and Cohomology Operations

Details The String Topology Loop Coproduct and Cohomology Operations The String Topology Loop Coproduct and Cohomology Operations

2007-12-03

arxiv.org/abs/0712.0212v1

Mathematics

Algebraic Topology

6 pages; submitted to the proceedings of the M.M.Postnikov memorial conference

Scientific paper

This note explores the interaction between cohomology operations in a generalized cohomology theory and a string topology loop coproduct dual to the Chas--Sullivan loop product. More precisely, we ask for a description for the failure of a given operation to commute with the loop coproduct, and will obtain a satisfactory answer in the case where the operation preserves both sums and products. Examples of such operations include the total Steenrod square in ordinary mod 2 cohomology and the Adams operations in K-theory.

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