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Topology/Geometry Seminar
Thursday, November 11, 2004
5:00-6:00pm,
115 Osmond (UP)
Rebecca Goldin
George Mason University, VA
Preorbifold Cohomology
Abstract: Orbifolds were first introduced in the 1950s to describe some of the simplest kinds of singularities that occur. They have become of interest lately because of their appearance in a wide array of mathematical fields. Traditional algebraic invariants (such as singular cohomology) do not record much of the structure of orbifolds. Recently Chen and Ruan introduced the "orbifold cohomology ring", which does capture orbifold information. However, the product structure of orbifold cohomology requires sophistication in algebro-geometric techniques, and is therefore difficult to compute. This talk is meant to be accessible to graduate students. I will explain how orbifolds occur in Hamiltonian geometry, and introduce the "preorbifold cohomology ring" of a Hamiltonian T-space, where T is a compact torus (a product of circles). This ring has the features that it is easy to compute, and it surjects onto the orbifold cohomology of orbifolds that arise by symplectic reduction. By computing the kernel of this map, we have developed a combinatorial way of describing the orbifold cohomology of a certain category of orbifolds. This work is joint with Allen Knutson and Tara Holm (both at University of CA, Berkeley).
