String topology operations
Summary
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.