The String Topology Loop Coproduct and Cohomology Operations

2007/12/03 by Anssi Lahtinen, Lahtinen, Anssi
Mathematics · #55N20 #55S25 (Primary) #57R19 (Secondary) #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.0712.0212

openalex publication_date 2007/12/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Twisted K-theory and loop group representations

Related

• Product and coproduct in string topology
• Intersection Multiplicity in Loop Spaces and the String Topology Coproduct
• A homotopy theoretic realization of string topology
• Adams operations in cohomotopy
• String topology via the coHochschild complex and local intersections