Related papers: Representing Bredon cohomology with local coeffici…

We study the Duflot filtration on the Borel equivariant cohomology of smooth manifolds with a smooth $p$-torus action. We axiomatize the filtration and prove analog of several structural results about equivariant cohomology rings in this…

We give an alternative to Postnikov's homotopy classification of maps from 3-dimensional CW-complexes to homogeneous spaces G/H of Lie groups. It describes homotopy classes in terms of lifts to the group G and is suitable for extending the…

We give a general framework of equivariant model category theory. Our groups G, called Hopf groups, are suitably defined group objects in any well-behaved symmetric monoidal category V. For any V, a discrete group G gives a Hopf group,…

Let p be an odd regular prime, and assume that the Lichtenbaum-Quillen conjecture holds for K(Z[1/p]) at p. Then the p-primary homotopy type of the smooth Whitehead spectrum Wh(*) is described. A suspended copy of the cokernel-of-J spectrum…

We classify pointed Hopf algebras of discrete corepresentation type over an algebraically closed field K with characteristic zero. For such algebras $H$, we explicitly determine the algebra structure up to isomorphism for the link…

We construct a degree-type otopy invariant for equivariant gradient local maps in the case of a real finite dimensional orthogonal representation of a compact Lie group. We prove that the invariant establishes a bijection between the set of…

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…

Local cohomology techniques in equivariant homotopy theory, introduced by John Greenlees, may be applied to understand homology of classifying spaces through other equivariant data. In this paper we relate the local cohomology filtration to…

We introduce a new construction, the isotropy groupoid, to organize the orbit data for split $\Gamma$-spaces. We show that equivariant principal $G$-bundles over split $\Gamma$-CW complexes $X$ can be effectively classified by means of…

We describe the cohomology groups of a homogeneous vector bundle $E$ on any Hermitian symmetric variety $X=G/P$ of ADE type as the cohomology of a complex explicitly described. The main tool is the equivalence between the category of…

Let $G$ be a split connected reductive group over the ring of integers of a finite unramified extension $K$ of $\mathbf{Q}_p$. Under a standard assumption on the Coxeter number of $G$, we compute the cohomology algebra of $G(\mathcal{O}_K)$…

A rigidity property for the homotopy invariant stable linear framed presheaves is established. As a consequence a variant of Gabber rigidity theorem is obtained for a cohomology theory representable in the motivic stable homotopy category…

A locally compact contraction group is a pair (G,f) where G is a locally compact group and f an automorphism of G which is contractive in the sense that the forward orbit under f of each g in G converges to the neutral element e, as n tends…

The main purpose of this article is to give the integral cohomology of classical principal congruence subgroups in SL(2,Z) as well as their analogues in the third braid group with local coefficients in symmetric powers of the natural…

Let n be any positive integer and p any prime. Also, let X be any spectrum and let K(n) denote the nth Morava K-theory spectrum. Then we construct a descent spectral sequence with abutment pi_*(L_{K(n)}(X)) and E_2-term equal to the…

On the basis of Brylinski's work, we introduce a notion of equivariant smooth Deligne cohomology group, which is a generalization of both the ordinary smooth Deligne cohomology and the ordinary equivariant cohomology. Using the cohomology…

We present a closed model structure for the category of pro-spectra in which the weak equivalences are detected by stable homotopy pro-groups. With some bounded-below assumptions, weak equivalences are also detected by cohomology as in the…

We develop cohomological and homological theories for a profinite group $G$ with coefficients in the Pontryagin dual categories of pro-discrete and ind-profinite $G$-modules, respectively. The standard results of group (co)homology hold for…

We study the local cohomology modules for the secant variety of lines of a smooth projective variety $Y$ and for higher secant varieties of smooth projective curves. We show that the local cohomological defect in the first case is related…

For a discrete group $\Gamma$ satisfying some finiteness conditions we give a Bredon projective resolution of the trivial module in terms of projective covers of the chain complex associated to certain posets of subgroups. We use this to…