EVENT DETAILS AND ABSTRACT

Title: Generalized String Topology and Derived Koszul Duality
Speaker: Aaron Royer
Speaker Info: University of Texas at Austin
Brief Description:
Special Note:
Abstract:

The existence of intersection-type operations on the homology of the free loop space of an oriented manifold was first brought to broad attention by Chas and Sullivan in the late 1990s. Building on the work of several previous authors, we place these structures in the modern context of highly structured spectra by constructing a lax symmetric monoidal functor from parametrized spaces (over a closed manifold) to symmetric spectra. Employing derived Koszul duality and the recently-developed theory of infinity categories, we give an alternative characterization of this ``generalized string topology'' functor, proving a coherence theorem for certain generalized Pontrjagin-Thom collapse maps in the process, and illuminating its role in parametrized stable homotopy theory.