Algebra/Topology Seminar

Speaker: Calista Bernard

Title: Twisted homology operations

Abstract: In the 70s, Fred Cohen and Peter May gave a description of the mod p homology of a free En-algebra in terms of certain homology operations, known as Dyer--Lashof operations and the Browder bracket. These operations capture the failure of the En multiplication to be strictly commutative, and they prove useful for computations. After reviewing the main ideas from May and Cohen's work, I will discuss a framework to generalize these operations to homology with certain twisted coefficient systems and give a complete classification of twisted operations for E-algebras. I will also explain computational results that show the existence of new operations for E2-algebras.