6 papers · 1 filter
The equivariant cohomology ring of the representation variety
Simon Gritschacher
We give a presentation of the -equivariant cohomology ring with -coefficients of the variety $\mathrm{Hom}(\mathbb{Z}^2,\mathrm{GL}_n(\mathbb…
Commuting varieties and the rank filtration of topological K-theory
Simon Gritschacher
We consider the space of -tuples of pairwise commuting elements in the Lie algebra of . We relate its one-point compactification to the subquotients of certain rank filtra…
A stable splitting for spaces of commuting elements in unitary groups
Alejandro Adem, José Manuel Gómez, Simon Gritschacher
We prove an analogue of Miller's stable splitting of the unitary group for spaces of commuting elements in . After inverting , the space $\text{Hom}(\mathbb{Z}^n,U…
Commuting matrices and Atiyah's Real K-theory
Simon Gritschacher, Markus Hausmann
We describe the -equivariant homotopy type of the space of commuting n-tuples in the stable unitary group in terms of Real K-theory. The result is used to give a complete calc…
Classifying spaces for commutativity of low-dimensional Lie groups
Omar Antolín-Camarena, Simon Gritschacher, Bernardo Villarreal
For each of the groups , we compute the integral and -cohomology rings of (the classifying space for commutativity of ), th…
A remark on the group-completion theorem
Simon Gritschacher
Suppose that is a topological monoid satisfying to which the McDuff-Segal group-completion theorem applies. This implies that a certain map $f: \mathbb{M}_{\i…