# Using Kronholm's Ideal to Compute Bredon Cohomology

## Document Type

Presentation Abstract

## Presentation Date

4-24-2023

## Abstract

We are interested in computing the $RO(C_2)$-graded Bredon cohomology of equivariant spaces which can be constructed as $\text{Rep}(C_2)$-complexes. Although a theorem of Kronholm dictates that this cohomology must be free, the pages of the spectral sequences converging to these cohomologies are not free, nor practial to compute.

However certain of these spaces, such as the Grassmannian manifold of $k$-planes inside of a given $C_2$-representation, have multiple constructions and so multiple spectral sequences which must converge to the same place. Using these multiple angles of attack and a generalization of the Poincare polynomial, we present an algorithm to advance these calculations in the much friendlier setting of a polynomial ring.

## Recommended Citation

Hogle, Eric, "Using Kronholm's Ideal to Compute Bredon Cohomology" (2023). *Colloquia of the Department of Mathematical Sciences*. 654.

https://scholarworks.umt.edu/mathcolloquia/654

## Additional Details

April 24, 2023 at 3:00 p.m. Math 103