Pontryagin-Thom for orbifolds

Pontryagin-Thom for orbifolds

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John Pardon, Princeton University 

What's Happening in Fine Hall

Zoom link: https://princeton.zoom.us/j/93918876391

Passcode: 803011

Closed manifolds M and M' are called *bordant* iff there exists a manifold N whose boundary is M\sqcup M'.  This defines an equivalence relation, called bordism, and manifolds modulo bordism form a group (the group operation being disjoint union).  Bordism groups come in various flavors depending on the sort of manifolds under consideration (unoriented, oriented, Spin, almost complex, stably framed, etc.), and are objects of central interest in algebraic topology.  One reason for this is the classical work of Pontryagin and Thom which identifies bordism groups with certain corresponding stable homotopy groups.  Extensions of the Pontryagin--Thom isomorphism to equivariant bordism groups has been known classically due to Conner--Floyd, Wasserman, tom Dieck, Brocker--Hook, and more recently Schwede.  I will discuss recent work which extends this isomorphism to bordism groups of orbifolds.  A key step will be to implement Spanier--Whitehead duality in a certain stable homotopy category of orbispaces.