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Enough vector bundles on orbispaces

John Pardon

An orbispace is a "space" which is locally the quotient of a topological space by a continuous action of a finite group. Familiar examples of orbispaces include orbifolds, (the analytifications of) Deligne--Mumford stacks over C, and moduli spaces of solutions to elliptic partial differential equations, as they appear in low-dimensional and symplectic topology. The fibers of a vector bundle over an orbispace are representations of its stabilizer groups. When do there exist vector bundles all of whose fiber representations are faithful? This condition is called having "enough" vector bundles, and plays an important role in the stable homotopy theory of orbispaces. In particular, it implies a Spanier--Whitehead duality functor in a certain stable homotopy category of orbispaces and a Pontryagin--Thom isomorphism for orbifold bordism groups.


Simons- SCGP Weekly Talk