Title: The String topology loop product through twisting cochains
Speaker: Dr. Micah Miller IISc, Bangalore
Date: 09 October 2012
Time: 3:30 pm- 4:30 pm
Venue: Department of Mathematics, LH-III
String topology is the study of the free loop space of a manifold LM. The loop product, defined on the homology of LM, is described intuitively as a combination of the intersection product on M and loop concatenation in the based loop space of M. However, since the intersection product is well-defined only on transversally intersecting chains, this description is incomplete. Brown’s theory of twisting cochains provides a chain model of a bundle in terms of the chains on the base and chains on the fiber. We extend this theory so that it can be applied to provide a model of the free loop space. We give a precise definition of the loop product defined at the chain level.