XXII WORKSHOP ON GEOMETRIC METHODS IN PHYSICS
29 JUNE - 5 JULY 2003, BIAŁOWIEŻA, POLAND
Alexander A. Voronov - String Topology
String Topology was introduced in 1999 by M. Chas and D. Sullivan, who
defined a new algebraic structure, that of a BU-algebra, on the free loop
space of a compact manifold. This structure describes interaction of
strings (loops) in the manifold and mimics the Gromov-Witten invariants in
a purely topological setting. I will discuss String Topology, as well as
a higher-dimensional generalization of it, where strings get replaced by
spheres. This generalization is related to Mochschild cohomology
and a
conjecture of Kontservich. Most part of this is joint work with Sullivan.