EVENT DETAILS AND ABSTRACT

Title: The Tate-Hochschild complex and algebraic string operations
Speaker: Manuel Rivera
Speaker Info: University of Miami
Brief Description:
Special Note:
Abstract:

Given any differential graded Frobenius algebra A we may construct an unbounded chain complex, called the Tate-Hochschild complex, which combines both the Hochschild cochain and chain complexes of A. This complex calculates the group of morphisms in the singularity category of A, i.e. in the Verdier quotient of the derived category of A-A-bimodules by the full subcategory of perfect modules. In this talk I will discuss how the natural algebraic structure of the Hochschild cochain complex of A extends to the full Tate-Hochschild complex. This will be explained from the perspective of string topology. String topology is concerned with geometric intersection type operations on the homology of the free loop space of a manifold. The algebraic structure of the Tate-Hochschild complex corresponds to carefully combining two fundamental operations in string topology: the Chas-Sullivan loop product with the more subtle Goresky-Hingston loop coproduct.