Related papers: A structure theorem for $RO(C_2)$-graded Bredon co…

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…

A surface with an involution can be viewed as a $C_2$-space where $C_2$ is the cyclic group of order two. Using the classification of $C_2$-surfaces given by Dugger, we compute the $RO(C_2)$-graded Bredon cohomology of all $C_2$-surfaces in…

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 $\underline{\mathbf{F}}_2$,…

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 study the $RO(G)$-graded Bredon cohomology of a point in the case where $G$ is a cyclic group of odd order, expanding on the information provided by previous studies. Our methods center on the purely algebraic aspects of this matter,…

The additive structure of the $RO(C_{pq})$-graded Bredon cohomology $S^0$ with coefficients in the constant Mackey functor was computed in \cite{BG19}. Using that computation, the ring structure in the positive degrees has been computed…

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 paper, we compute the $RO(C_{pq})$-graded cohomology of $C_{pq}$-orbits. We deduce that in all the cases the Bredon cohomology groups are a function of the fixed point dimensions of the underlying virtual representations. Further,…

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 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…

Let $C_n$ denote a cyclic group of order $n$. In this paper we investigate modules and chain complexes over the constant integral Mackey functor $\underline{\mathbb{Z}}$ and perform some related homological calculations. Along the way we…

We describe the main properties of the $RO(C_2\times \Sigma_2)$-graded cohomology ring of a point and apply the results to compute the subring of motivic classes given by the Bredon motivic cohomology of real numbers and to compute…

Following the Hu-Kriz method of computing the $C_2$ genuine dual Steenrod algebra $(H\mathbf F_2)_{\bigstar}(H\mathbf F_2)$, we calculate the $C_4$ equivariant Bredon cohomology of the classifying space $\mathbf R P^{\infty…

For the cyclic group $C_2$ we give a complete description of the derived category of perfect complexes of modules over the constant Mackey ring $\underline{\mathbb{Z}/\ell}$, for $\ell$ a prime. This is fairly simple for $\ell$ odd, but for…

We are interested in computing the Bredon cohomology with coefficients in the constant Mackey functor $\underline{ \mathbb{F}_2}$ for equivariant $\text{Rep}(C_2)$ spaces, in particular for Grassmannian manifolds of the form…

We calculate the ordinary $C_2$-cohomology, with Burnside ring coefficients, of $CP_{C_2}^\infty = B_{C_2} U(1)$, the complex projective space, a model for the classifying space for $C_2$-equivariant complex line bundles. The…

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…

Let $G$ be a finite group and $V$ be a $G$-representation. We investigate the $RO(G)$-graded Bredon cohomology with constant integral coefficients of the space of ordered configurations in $V$. In the case that $V$ contains a trivial…

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…