String topology operations

Abstract

String topology studies the topology of the free loop space of a manifold and related spaces. The merging and splitting of these strings endows the homology of these spaces with a rich structure. In this thesis we give a construction of these string operations in the more general case where one also allows open strings with endpoints restricted to submanifolds, known as branes. By doing this we solve Godin's conjecture A about the existence of string operations in this general case. Finally, we discuss results on explicitly determining the structure coming from these operations. In three postscripts, we extend this work: (1) we calculate the string topology structure of some Lie groups, (2) of compact oriented surfaces and (3) give an alternative simpler construction of these operations based on B odigheimer's radial slit configuration model of the moduli space of Riemann surfaces with boundary.