## Orbifold String Topology I

- Date: 05/02/2007

Bernardo Uribe (Universidad de los Andes)

University of British Columbia

In these two lectures I will survey my recent work with Lupercio and

Xicotencatl on the properties of the homology of the free loop space of

an orbifold. In the first lecture I will review the work of Chas and

Sullivan on string topology and I will describe how this theory could

be generalized to the space of free loops on an orbifold. I will also

review the Hochschild version of string topology due to Cohen and Jones

and how this construction could also be generalized to the orbifold

case. At the end of the lecture I will show some simple examples to get

a flavor of the theory. In the second lecture I will show how the

orbifold string topology on the symmetric product gives rise to a ring

structure on the cohomology of the inertia orbifold; this we have

coined the virtual cohomology. Then I will explain the relation between

the virtual cohomology and the Chen-Ruan cohomology. To finish I will

show how to calculate in general the virtual cohomology, and I will

give some examples.

Algebraic Topology Seminar 2007