Related papers: A spectral sequence for Dehn fillings

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…

For a pair $(G,N)$ of a group $G$ and its normal subgroup $N$, we consider the space of quasimorphisms and quasi-cocycles on $N$ non-extendable to $G$. To treat this space, we establish the five-term exact sequence of cohomology relative to…

Spectral sequences are a common tool to compute cohomology spaces, but higher structure is often lost on the way. In this article we exhibit a strategy to retain the higher structure on the cohomology, which works in case the chain complex…

Let $G$ be a group and $S$ a unital epsilon-strongly $G$-graded algebra. We construct spectral sequences converging to the Hochschild (co)homology of $S$. Each spectral sequence is expressed in terms of the partial group (co)homology of $G$…

A degeneration of compact Kaehler manifolds gives rise to a monodromy action on Betti moduli space H^1(X, G) = Hom(\pi_1(X),G)/G over smooth fibres with a complex algebraic structure group G being either abelian or reductive. Assume that…

We investigate the genera of quotient curves $\mathcal H_q/G$ of the $\mathbb F_{q^2}$-maximal Hermitian curve $\mathcal H_q$, where $G$ is contained in the maximal subgroup $\mathcal M_q\leq{\rm Aut}(\mathcal H_q)$ fixing a pole-polar pair…

In this paper the Serre spectral sequence of Moerdijk and Svensson is extended from Bredon cohomology to RO(G)-graded cohomology for finite groups G. Special attention is paid to the case G=Z/2 where the spectral sequence is used to compute…

We study the electromagnetic (EM) duality from $6$ derivative theory with homogeneous disorder. We find that with the change of the sign of the coupling parameter $\gamma_1$ of the $6$ derivative theory, the particle-vortex duality with…

We generalize Quillen's $F$-isomorphism theorem, Quillen's stratification theorem, the stable transfer, and the finite generation of cohomology rings from finite groups to homotopical groups. As a consequence, we show that the category of…

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…

We define a new condition on relatively hyperbolic Dehn filling which allows us to control the behavior of a relatively quasiconvex subgroups which need not be full. As an application, in combination with a recent result of Cooper and…

We introduce a cochain complex for ample groupoids $\mathcal G$ using a flat resolution defining their homology with coefficients in $\mathbb Z$. We prove that the cohomology of this cochain complex with values in a $\mathcal G$-module $M$…

We consider a compact complex manifold $M$, and introduce the notion of two holomorphic Banach bundles $E,F$ over $M$ being compact perturbations of one another. Given two such bundles we show that if the cohomology groups $H^q(M,E)$ are…

Hyperbolic Dehn surgery and the bending procedure provide two ways which can be used to describe hyperbolic deformations of a complete hyperbolic structure on a 3-manifold. Moreover, one can obtain examples of non-Haken manifolds without…

We give three infinite families of examples of nonhyperbolic Dehn fillings on hyperbolic manifolds. A manifold in the first family admits two Dehn fillings of distance two apart, one of which is toroidal and annular, and the other is…

Let $(M,g)$ an open and oriented riemannian manifold. The aim of this paper is to study some properties of the two following sequences of $L^2$ cohomology groups: $H^i_{2,m\rightarrow M}(M,g)$ defined as the image…

Given a complex reductive group G, Borel subgroup B, and topological surface S with boundary dS, we study the "Betti spectral category" DCoh_N(Loc_G(S, dS)) of coherent sheaves with nilpotent singular support on the character stack of…

We apply representation theory to study the homology of equivariant Dehn-fillings of a given finite, regular cover of a compact 3-manifold with boundary a torus. This yields a polynomial which gives the rank of the part of the homology…

For a semisimple real Lie group $G$, we study topological properties of moduli spaces of polystable parabolic $G$-Higgs bundles over a Riemann surface with a divisor of finitely many distinct points. For a split real form of a complex…

The dynamics of high partonic density QCD is presented considering, in the double logarithm approximation, the parton recombination mechanism built in the AGL formalism, developed including unitarity corrections for the nucleon as well for…