Transformation Groups Seminar

Speaker: Kumar Sannidhya Shukla (Western)

"Complexity 0 torus action on manifolds (Part 3)"

Time: 10:30

Room: MC 108

Let T be an n-dimensional torus acting on a ‘nice’ 2n-manifold M effectively, with nonempty set of fixed points and suppose that all the isotropy groups are connected. If the action satisfies another hypothesis (equivariant formality) then the quotient space M/T has the structure of a homology cell complex and is in fact a homology disk. In this talk we will give first discuss some general facts about orbits of torus actions on manifolds and about locally standard actions. Then using the Atiyah-Bredon-Franz-Puppe sequence we give a detailed proof of the fact that under the assumptions stated above, M/T is a homology disk.