Related papers: A Spectral sequence for polynomially bounded cohom…

We describe how the result in [1] extends to prove the existence of a Serre type spectral sequence converging to the symplectic homology SH_*(M) of an exact Sub-Liouville domain M in a cotangent bundle T*N. We will define a notion of a…

The aim of this paper is to construct and examine three candidates for local-to-global spectral sequences for the cohomology of diagrams of algebras with directed indexing. In each case, the $E^2$ -terms can be viewed as a type of local…

In this paper we develop the basic homotopy theory of G-symmetric spectra (that is, symmetric spectra with a G-action) for a finite group G, as a model for equivariant stable homotopy with respect to a G-set universe. This model lies in…

We construct a spectral sequence for L2-type cohomology groups of discrete measured groupoids. Based on the spectral sequence, we prove the Hopf-Singer conjecture for aspherical manifolds with poly-surface fundamental groups. More…

Let $1 \to N \to G \to G/N \to 1$ be a short exact sequence of countable discrete groups and let $B$ be any $G$-$C^*$-algebra. In this paper, we show that the strong Novikov conjecture with coefficients in $B$ holds for such a group $G$…

Let G denote a complex, semisimple, simply-connected group. We identify the equivariant quantum differential equation for the cotangent bundle to the flag variety of G with the affine Knizhnik-Zamolodchikov connection of Cherednik and…

Let $A$ be a left-symmetric (resp. Novikov) algebra, $E$ be a vector space containing $A$ as a subspace and $V$ be a complement of $A$ in $E$.The extending structures problem which asks for the classification of all left-symmetric (resp.…

Let $H$ be a Hopf algebra. We consider $H$-equivariant modules over a Hopf module category $\mathcal C$ as modules over the smash extension $\mathcal C\# H$. We construct Grothendieck spectral sequences for the cohomologies as well as the…

We develop some new aspects of cohomology in the context of semi-abelian categories: we establish a Hochschild-Serre 5-term exact sequence extending the classical one for groups and Lie algebras; we prove that an object is perfect if and…

In this paper, we introduce the localized slice spectral sequence, a variant of the equivariant slice spectral sequence that computes geometric fixed points equipped with residue group actions. We prove convergence and recovery theorems for…

In this paper the authors investigate the structure the restricted Lie algebra cohomology of p-nilpotent Lie algebras with trivial p-power operation. Our study is facilitated by a spectral sequence whose $E_{2}$-term is the tensor product…

We extend the theory of equivariant orthogonal spectra from finite groups to profinite groups, and more generally from compact Lie groups to compact Hausdorff groups. The G-homotopy theory is "pieced together" from the G/U-homotopy theories…

A cohomology theory associated to a holomorphic Poisson structure is the hypercohomology of a bi-complex where one of the two operators is the classical $\overline\partial$-operator, while the other operator is the adjoint action of the…

We show that for each discrete group G, the rational assembly map K_*(BG) \otimes Q \to K_*(C*_{max} G) \otimes \Q is injective on classes dual to the subring generated by cohomology classes of degree at most 2 (identifying rational…

Let $A$ be a commutative algebra over the field ${\mathbb F}_2 = {\mathbb Z}/2$. We show that there is a natural algebra homomorphism $\ell (A) \to HC^-_*(A)$ which is an isomorphism when $A$ is a smooth algebra. Thus, the functor $\ell$…

For a motivic spectrum $E\in \mathcal{SH}(k)$, let $\Gamma(E)$ denote the global sections spectrum, where $E$ is viewed as a sheaf of spectra on $\mathrm{Sm}_k$. Voevodsky's slice filtration determines a spectral sequence converging to the…

We adapt and generalise results of Loganathan on the cohomology of inverse semigroups to the cohomology of ordered groupoids. We then derive a five-term exact sequence in cohomology from an extension of ordered groupoids, and show that this…

We develop the Hochschild analogue of the coniveau spectral sequence and the Gersten complex. Since Hochschild homology does not have devissage or A^1-invariance, this is a little different from the K-theory story. In fact, the rows of our…

We study the spectral sequence associated to the filtration by powers of the augmentation ideal on the (twisted) equivariant chain complex of the universal cover of a connected CW-complex X. In the process, we identify the d^1 differential…

The aim of this paper is to introduce and study a geometric spectral sequence in Khovanov homology. The construction was motivated by a similar spectral sequence from Khovanov homology to Heegaard Floer homology.