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

We construct a motivic Eilenberg-MacLane spectrum with a highly structured multiplication over smooth schemes over Dedekind domains which represents Levine's motivic cohomology. The latter is defined via Bloch's cycle complexes. Our method…

Let $\mathfrak{L}$ be a Leibniz algebra, $E$ a vector space and $\pi : E \to \mathfrak{L}$ an epimorphism of vector spaces with $ \mathfrak{g} = {\rm Ker} (\pi)$. The global extension problem asks for the classification of all Leibniz…

The Leray-Serre and the Eilenberg-Moore spectral sequences are fundamental tools for computing the cohomology of a group or, more generally, of a space. We describe the relationship between these two spectral sequences when both of them…

We use the $C_2$-equivariant Adams spectral sequence to compute part of the $C_2$-equivariant stable homotopy groups $\pi^{C_2}_{n,n}$. This allows us to recover results of Bredon and Landweber on the image of the geometric fixed-points map…

We recall how a description of local coefficients that Eilenberg introduced in the 1940s leads to spectral sequences for the computation of homology and cohomology with local coefficients. We then show how to construct new equivariant…

We prove an analogue of the de Rham theorem for the extended L^2-cohomology introduced by M. Farber. This is done by establishing that the de Rham complex over a compact closed manifold with coefficients in a flat Hilbert bundle E of…

For strongly even $\mathbb{E}_{\infty}^{C_2}$-rings $E$ we show that any homotopy ring map $\mathrm{MU} \to E^e$ lifts to an $\mathbb{E}_{\rho}$-map $\mathrm{MU}_{\mathbb{R}} \to E$. This refines the Hahn-Shi Real orientations of Lubin-Tate…

In this paper we describe the Hopf algebras on planar binary trees used to renormalize the Feynman propagators of quantum electrodynamics, and the coaction which describes the renormalization procedure. Both structures are related to some…

We prove that a depth two Hopf subalgebra K of a semisimple Hopf algebra H is normal (where the ground field $k$ is algebraically closed of characteristic zero). This means on the one hand that a Hopf subalgebra is normal when inducing…

Let $X=G/H$ be a reductive homogeneous space with $H$ noncompact, endowed with a $G$-invariant pseudo-Riemannian structure. Let $L$ be a reductive subgroup of $G$ acting properly on $X$ and $\Gamma$ a torsion-free discrete subgroup of $L$.…

For complex parallelisable manifolds $\Gamma\backslash G$, with $G$ a solvable or semisimple complex Lie group, the Fr\"olicher spectral sequence degenerates at the second page. In the solvable case, the de-Rham cohomology carries a pure…

We introduce the notion of a Galois extension of commutative S-algebras (E_infty ring spectra), often localized with respect to a fixed homology theory. There are numerous examples, including some involving Eilenberg-Mac Lane spectra of…

There is only one nontrivial localization of $\pi_*S_{(p)}$ (the chromatic localization at $v_0=p$), but there are infinitely many nontrivial localizations of the Adams $E_2$ page for the sphere. The first non-nilpotent element in the $E_2$…

We construct a new spectrum of units for a commutative symmetric ring spectrum that detects the difference between a periodic ring spectrum and its connective cover. It is augmented over the sphere spectrum. The homotopy cofiber of its…

An explicit gerbe-theoretic description of the super-$\sigma$-models of the Green-Schwarz type is proposed and its fundamental structural properties, such as equivariance with respect to distinguished isometries of the target supermanifold…

We realize the simple Lie superalgebra G(3) as supersymmetry of various geometric structures, most importantly super-versions of the Hilbert-Cartan equation (SHC) and Cartan's involutive PDE system that exhibit G(2) symmetry. We provide the…

The cyclic (co)homology of Hopf algebras is defined by Connes and Moscovici [math.DG/9806109] and later extended by Khalkhali et.al [math.KT/0306288] to admit stable anti-Yetter-Drinfeld coefficient module/comodules. In this paper we will…

In this note, we consider the Lyndon--Hochschild--Serre spectral sequence corresponding to the first Frobenius kernel of an algebraic group G, computing the extensions between simple $G$-modules. We state and discuss a conjecture that…

We consider Picard surfaces, locally symmetric varieties $S_{\Gamma}$ attached to the Lie group SU(2,1), and we construct explicit differential forms on $S_{\Gamma}$ representing Eisenstein classes, i.e. cohomology classes restricting…

Let $n \geq 1$, $p$ a prime, and $T(n)$ any representative of the Bousfield class of the telescope $v_n^{-1}F(n)$ of a finite type $n$ complex. Also, let $E_n$ be the Lubin-Tate spectrum, $K(E_n)$ its algebraic $K$-theory spectrum, and…