MCA Prize Lecture

Friday, July 23, 12:15 ~ 13:15 UTC-3

Pontryagin-Thom for orbifold bordism

John Pardon

Princeton University, USA   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

The classical Pontryagin-Thom isomorphism equates manifold bordism groups with corresponding stable homotopy groups. Extensions of the Pontryagin-Thom isomorphism to equivariant bordism groups have been known classically due to Conner-Floyd, Wasserman, tom Dieck, Brocker-Hook, and more recently Schwede. I will discuss work which establishes a Pontryagin-Thom isomorphism for orbispaces (an orbispace is a "space" which is locally modelled on Y/G for Y a space and G a finite group; examples of orbispaces include orbifolds and moduli spaces of pseudo-holomorphic curves). A key step will be to implement Spanier-Whitehead duality in a certain stable homotopy category of orbispaces.

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