Geometry and Topology
Speaker: Jeff Carlson (Western)
"An 19th-century approach to equivariant complex cobordism"
Time: 15:30
Room: MC 107
Despite its being an important universal object in equivariant homotopy theory, concrete generators-and-relations presentations for the coefficient ring of equivariant complex cobordism with respect to a compact abelian Lie group $G$ are still known only for finite $G$.
For $G$ a torus, Ginzburg--Karshon--Tolman observed that the well-known fixed-point integral localization formula of Atiyah--Bott--Berline--Vergne determines a naive upper bound on this ring, and the geometrically important case of a so-called GKM action, leaning on work of Darby, Carlson--Gamse--Karshon showed this bound is an equality.
The author has recently shown the same for semifree circle actions with isolated fixed points, unexpectedly recovering a 2004 result of Sinha with a new proof that is classical in the literal sense: it would have been accessible in the era of Beethoven. In this talk we will give background and sketch this proof.
Mathematics Calendar 
Week of October 6, 2019
