Related papers: A Cartan-Eilenberg spectral sequence for a non-nor…

Noncommutative K\"ahler structures were recently introduced as an algebraic framework for studying noncommutative complex geometry on quantum homogeneous spaces. In this paper, we introduce the notion of a \emph{compact quantum homogeneous…

We investigate the homology of a congruence subgroup Gamma of SL_3(Z) with coefficients in the Steinberg modules St(Q^3) and St(E^3), where E is a real quadratic field and the coefficients are Q. By Borel-Serre duality, H_0(Gamma, St(Q^3))…

We construct an isomorphism between the wrapped higher-dimensional Heegaard Floer homology of $\kappa$-tuples of cotangent fibers and $\kappa$-tuples of conormal bundles of homotopically nontrivial simple closed curves in $T^*\Sigma$ with a…

In this work, we develop systematically the ``Dirichlet Hopf algebra of arithmetics'' by dualizing addition and multiplication maps. We study the additive and multiplicative antipodal convolutions which fail to give rise to Hopf algebra…

We introduce a variant of the slice spectral sequence which uses only regular slice cells, and state the precise relationship between the two spectral sequences. We analyze how the slice filtration of an equivariant spectrum that is…

An analog of Kreimer's coproduct from renormalization of Feynman integrals in quantum field theory, endows an analog of Kontsevich's graph complex with a dg-coalgebra structure. The graph complex is generated by orientation classes of…

We describe an iterable construction of THH for an E_n ring spectrum. The reduced version is an iterable bar construction and its n-th iterate gives a model for the shifted cotangent complex at the augmentation, representing reduced…

For an $\E$-ring spectrum $R$ and a map $f:X\to Pic(R)$ of spaces, the Thom spectrum $\T f$ is a comodule over $R\otimes\Si X$. In this parper we study the topological coHochschild homology of $R\otimes\Si X$ with coefficient $\T f$. More…

We study how the combinatorial structure of the Salvetti complexes of the braid arrangements are related to homotopy theoretic properties of iterated loop spaces. We prove the skeletal filtrations on the Salvetti complexes of the braid…

We recall the notion of twisted parametrized spectra defined by Douglas and provide a sufficient condition for an $\infty$-category of twisted parametrized module spectra to be untwisted over an even-periodic $E_2$-ring. It is an easy…

This is a survey paper on cohomology theories for $A_\infty$ and $E_\infty$ ring spectra. Different constructions and main properties of topological Andr\'e-Quillen cohomology and of topological derivations are described. We give sample…

We define $H$-Galois extensions for $k$-linear categories and a Hopf algebra $H$ and prove the existence of a Grothendieck spectral sequence for Hochschild-Mitchell cohomology, related to this situation. This spectral sequence is…

We make some computations in stable motivic homotopy theory over Spec \mathbb{C}, completed at 2. Using homotopy fixed points and the algebraic K-theory spectrum, we construct a motivic analogue of the real K-theory spectrum KO. We also…

We introduce the notion of an \emph{$n$-dimensional mixed dihedral group}, a general class of groups for which we give a graph theoretic characterisation. In particular, if $H$ is an $n$-dimensional mixed dihedral group then the we…

For a compact, oriented, hyperbolic $n$-manifold $(M,g)$, realised as $M= \Gamma \backslash \mathbb{H}^{n}$ where $\Gamma$ is a torsion-free cocompact subgroup of $SO(n,1)$, we establish and study a relationship between differential…

We give a simple universal property of the multiplicative structure on the Thom spectrum of an $n$-fold loop map, obtained as a special case of a characterization of the algebra structure on the colimit of a lax $\mathcal{O}$-monoidal…

Let $\mathcal{A}_1$ and $\mathcal{A}_2$ be standard operator algebras on complex Banach spaces $X_1$ and $X_2$, respectively. For $k\geq2$, let $(i_1,...,i_m)$ be a sequence with terms chosen from $\{1,\ldots,k\}$, and assume that at least…

Let $E$ be an elliptic curve defined over a field $K$ (with $char(K)\neq 2$) given by a Weierstrass equation and let $P=(x,y)\in E(K)$ be a point. Then for each $n$ $\geq 1$ and some $\gamma \in K^{\ast }$ we can write the $x$- and…

We study the structure of the $E_2$-term of the Rothenberg-Steenrod spectral sequence converging to the mod 3 cohomology of the classifying space of the compact, connected, simply connected, exceptional Lie group of rank 6.

Let $\Gamma$ be a $T$-ideal of identities of an affine PI-algebra over an algebraically closed field $F$ of characteristic zero. Consider the family $\mathcal{M}_{\Gamma}$ of finite dimensional algebras $\Sigma$ with $Id(\Sigma) = \Gamma$.…