Sophie Kriz, University of Michigan

Resumen: I will describe my construction of a certain “weak orientation class” and use it to derive a new relation between Borel and Mackey cohomology. (Some related observations were also made in [Hill-Hopkins-Ravenel: On the non-existence of elements of Kervaire invariant 1].) One application is a new completion theorem for complex cobordism modules that does not involve higher derived functors. Applying this result to Morava K(n)-theory, I will describe my recent counterexample to the homotopical version of the evenness conjecture for equivariant complex cobordism. I will also describe the relationship between this result and previous work on various forms of the evenness conjecture, including the recent theorems by Samperton and Uribe.

https://sites.google.com/view/equivariant-bordism-and-applic/inicio