Pontryagin--Thom for orbifold bordism

John Pardon, Princeton University

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The classical Pontryagin–Thom isomorphism equates manifold bordism groups with corresponding stable homotopy groups.  This construction moreover generalizes to the equivariant context.  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).  This involves defining a category of orbispectra and an involution of this category