Related papers: $C_{2^n}$-equivariant rational stable stems and ch…

This is a survey of recent results on classification of compact quantum groups of Lie type, by which we mean quantum groups with the same fusion rules and dimensions of representations as for a compact connected Lie group $G$. The…

Considering the potential equivariant formality of the left action of a connected Lie group $K$ on the homogeneous space $G/K$, we arrive through a sequence of reductions at the case $G$ is compact and simply-connected and $K$ is a torus.…

The equivariant coarse index is well-understood and widely used for actions by discrete groups. We extend the definition of this index to general locally compact groups. We use a suitable notion of admissible modules over $C^*$-algebras of…

We show that the category of rational G-spectra for a torus G is Quillen equivalent to an explicit small and practical algebraic model, thereby providing a universal de Rham model for rational G-equivariant cohomology theories. The result…

For the split group $G_{2}$ defined over $\mathbb{Z},$ we show that the de Rham cohomology ring of $B(G_{2})_{\mathbb{F}_{2}}$ is isomorphic to the singular cohomology ring with $\mathbb{F}_{2}$-coefficients of $B(G_{2})_{\mathbb{C}}.$ For…

This monograph introduces a framework for genuine proper equivariant stable homotopy theory for Lie groups. The adjective `proper' alludes to the feature that equivalences are tested on compact subgroups, and that the objects are built from…

We study closed, connected, spin 4-manifolds up to stabilisation by connected sums with copies of $S^2 \times S^2$. For a fixed fundamental group, there are primary, secondary and tertiary obstructions, which together with the signature…

An action of a torus T on a manifold M is locally standard if, at each point, the stabilizer is a sub-torus and the non-zero isotropy weights are a basis to its weight lattice. The quotient M/T is then a manifold-with-corners, decorated by…

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…

In this paper, we prove an equivariant version of the classical Dold-Thom theorem. Associated to a finite group, a CW-complex on which this group acts and a covariant coefficient system in the sense of Bredon, we functorially construct a…

Coincident root loci are subvarieties of $S^d(C^2)$--the space of binary forms of degree $d$--labelled by partitions of $d$. Given a partition $\lambda$, let $X_\lambda$ be the set of forms with root multiplicity corresponding to $\lambda$.…

We compute the cohomology groups of the automorphism group of the free group $F_n$, with coefficients in arbitrary tensor products of the standard representation $H_1(F_n, \mathbb{Q})$ and its dual, in a range where $n$ is sufficiently…

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…

We give the stable splitting of the complex connective K-theory of the classifying space of special orthogonal groups on even dimensions.

The cohomology of the pure string motion group PSigma_n admits a natural action by the hyperoctahedral group W_n. Church and Farb conjectured that for each k > 0, the sequence of degree k rational cohomology groups of PSigma_n is uniformly…

We describe in terms of generators and relations the ring structure of the $RO(C_2)$-graded $C_2$-equivariant stable stems $\pi_\star^{C_2}$ modulo the ideal of all nilpotent elements. As a consequence, we also record the ring structure of…

Using the Berline-Vergne integration formula for equivariant cohomology for torus actions, we prove that integrals over Grassmannians (classical, Lagrangian or orthogonal ones) of characteristic classes of the tautological bundle, can be…

Over the complex numbers, we compute the $C_2$-equivariant Bredon motivic cohomology ring with $\mathbb{Z}/2$ coefficients. By rigidity, this extends Suslin's calculation of the motivic cohomology ring of algebraically closed fields of…

We describe the ring structure of the rational cohomology of the Torelli groups of the manifolds $\#^g S^n \times S^n$ in a stable range, for $2n \geq 6$. Some of our results are also valid for $2n=2$, where they are closely related to…

We introduce the notion of Q-filtrable varieties: projective varieties with a torus action and a finite number of fixed points, such that the cells of the associated Bialynicki-Birula decomposition are all rationally smooth. Our main…