Related papers: Bigraded Poincar\'e polynomials and the equivarian…

We compute the $RO(C_2)$-graded Bredon cohomology of certain families of real and complex $C_2$-equivariant Grassmannians.

We compute the equivariant cohomology of complex projective spaces associated to finite-dimensional representations of $C_2$, using ordinary cohomology graded on representations of the fundamental groupoid, with coefficients in the Burnside…

We give a complete description of the bigraded Bredon cohomology ring of smooth projective real quadrics, with coefficients in the constant Mackey functor $ \mathbf{Z} $. These invariants are closely related to the integral motivic…

We compute the $RO(C_p \times C_p)$-graded Bredon cohomology of equivariant universal and classifying spaces associated to families of subgroups, with coefficients in the constant Mackey functor $\underline{\mathbb{F}_p}$. An explicit…

We obtain a characterization of Maximal and Galois-Maximal $C_2$-spaces (including real algebraic varieties) in terms of $\operatorname{RO}(C_2)$-graded cohomology with coefficients in the constant Mackey functor $\underline{\mathbf{F}}_2$,…

We extend Ravenel-Wilson Hopf ring techniques to $C_2$-equivariant homotopy theory. Our main application and motivation is a computation of the $RO(C_2)$-graded homology of $C_2$-equivariant Eilenberg-MacLane spaces. The result we obtain…

In this, the second of three papers about $C_2$-equivariant complex quadrics, we calculate the equivariant ordinary cohomology of smooth symmetric quadrics graded on the representation ring of $\Pi BU(1)$ and with coefficients in the…

Let $C_2$ be the cyclic group of order two. We present a structure theorem for the $RO(C_2)$-graded Bredon cohomology of $C_2$-spaces using coefficients in the constant Mackey functor $\underline{\mathbb{F}_2}.$ We show that, as a module…

Let $C_2$ be the cyclic group of order two. We show that the $RO(C_2)$-graded Bredon cohomology of a finite Rep($C_2$)-complex is free as a module over the cohomology of a point when using coefficients in the constant Mackey functor…

In this note we state corrected and expanded versions of our previous results on power operations for $C_2$-equivariant Bredon homology with coefficients in the constant Mackey functor on $\mathbb{F}_2$. In particular, we give a version of…

We calculate the representation-graded Bredon homology rings of all elementary abelian 2-groups with coefficients in the constant mod-2 Mackey functor. We exhibit minimal presentations for these rings as quotients of the polynomial algebra…

We establish a novel approach to computing $G$-equivariant cohomology for a finite group $G$, and demonstrate it in the case that $G = C_{p^n}$. For any commutative ring spectrum $R$, we prove a symmetric monoidal reconstruction theorem for…

We study moduli spaces of (semi-)stable representations of one-point extensions of quivers by rigid representations. This class of moduli spaces unifies Grassmannians of subrepresentations of rigid representations and moduli spaces of…

Let $C_2$ denote the cyclic group of order two. Given a manifold with a $C_2$-action, we can consider its equivariant Bredon $RO(C_2)$-graded cohomology. In this paper, we develop a theory of fundamental classes for equivariant submanifolds…

We calculate the ordinary $C_2$-cohomology, with Burnside ring coefficients, of $BU(2)$, the classifying space for $C_2$-equivariant complex 2-plane bundles, using an extended grading that allows us to capture a more natural set of…

Over the real numbers with $\Z/2-$coefficients, we compute the $C_2$-equivariant Borel motivic cohomology ring, the Bredon motivic cohomology groups and prove that the Bredon motivic cohomology ring of the real numbers is a proper subring…

We compute the additive structure of the $\mathrm{RO}(C_n)$-graded Bredon equivariant cohomology of the equivariant classifying space $B_{C_n}\mathrm{SU}(2)$, for any $n$ that is either prime or a product of distinct odd primes, and we also…

In this, the last of three papers about $C_2$-equivariant complex quadrics, we complete the calculation of the equivariant ordinary cohomology of smooth symmetric quadrics in the cases where the fixed sets have more than two components.…

This paper determines the RO(G)-graded Eilenberg-MacLane cohomology of the real, infinite, equivariant Grassmannians in the case G=Z/2. Possible connections with motivic characteristic classes for quadratic bundles are briefly discussed.

We use the $C_2$-equivariant Adams spectral sequence to compute part of the $C_2$-equivariant stable homotopy groups $\pi^{C_2}_{n,n}$. This allows us to recover results of Bredon and Landweber on the image of the geometric fixed-points map…