arXiv research

Establishes a rank inequality between knot Floer homologies of freely 2-periodic knots and their quotients.

Seidel-Smith and Hendricks used equivariant Floer cohomology to define some spectral sequences from symplectic Khovanov homology and Heegaard Floer homology. These spectral sequences give rise to Smith-type inequalities. Similar-looking spectral sequences have been defined by Lee, Bar-Natan, Ozsváth-Szabó, Lipshitz-Tre…

This paper is based on the paper "Locally free sheaves on complex supermanifolds" of A.L.Onishchik, E.G. Vishnyakova, where two classification theorems for locally free sheaves on supermanifolds were proved and a spectral sequence for a locally free sheaf of modules E was obtained. We consider another filtration of the…

Study on spectral sequence for abelian Lie group actions, with bounds and applications.

We explain how to compute the Jones polynomial of a link from one of its grid diagrams and we observe a connection between Bigelow's homological definition of the Jones polynomial and Kauffman's definition of the Jones polynomial. Consequently, we prove that the Maslov grading on the Seidel-Smith symplectic link invari…

Constructs Serre spectral sequence for bounded cohomology.

Develops a spectral sequence for Lie group actions on manifolds.

Defines spectral sequences for fiberwise Dirac operators and proves adiabatic limit formula.

Proves spectral sequence for real Heegaard Floer homology.

Describes the relationship between two spectral sequences and their joint refinement.

New spectral sequences define knot invariants.

Introduces a framework for rational homotopy theory in diffeological spaces.

New spectral sequence connects to topological Hochschild homology.

Study Bergman and spectral kernels for non-compact complex manifolds.

Study finite group actions on 4-manifolds, finding rank bounds.

The abstract discusses a spectral sequence for Lie algebroids.

We prove that the inclusion of every closed exact Lagrangian with vanishing Maslov class in a cotangent bundle is a homotopy equivalence. We start by adapting an idea of Fukaya-Seidel-Smith to prove that such a Lagrangian is equivalent to the zero section in the Fukaya category with integral coefficients. We then study…

Given a compact Kaehler manifold, we consider the complement U of a divisor with normal crossings and a unitary local system V on it. We consider a differential graded Lie algebra (DGLA) of forms with holomorphic logarithmic singularities and vanishing residues. We construct a spectral sequence corresponding to the ant…

Study on spectral sequence of Iwasawa manifold and its deformations.

New concordance invariant from spectral sequence on Khovanov homology.

Spectral sequence connects knot homologies via algebraic geometry.

Incompatible operations affect Khovanov homology and spectral sequences.

The spectral sequence's $E_k$-page is a link invariant for $k\ge 3$.

The paper explores spectral sequences of complex manifolds with special metrics.

Cohomological and homological spectral sequences are shown to be isomorphic.

Let $M$ be an exact symplectic manifold equal to a symplectization near infinity and having stably trivializable tangent bundle, and $φ$ be an exact symplectomorphism of $M$ which, near infinity, is equal to either the identity or the symplectization of a contactomorphism $\hatφ$ such that neither $\hatφ$ nor $\hatφ^2$…

Spectral sequence connects knot homologies to quotient knots.

Let X be a finite CW-complex, denote its fundamental group by G. Let R be an n-dimensional complex repesentation of G. Any element A of the first cohomology group of X with complex coefficients gives rise to the exponential deformation of the representation R, which can be considered as a curve in the space of represen…

The paper examines the topology of quaternionic toric actions on manifolds.

Computes immersions of $C_2$-projective spaces using K-theory.

We derive a blow-up formula for the de Rham cohomology of a local system of complex vector spaces on a compact complex manifold. As an application, we obtain the blow-up invariance of $E_{1}$-degeneracy of the Hodge-de Rham spectral sequence associated to a local system of complex vector spaces.

Szabó recently introduced a combinatorially-defined spectral sequence in Khovanov homology. After reviewing its construction and explaining our methodology for computing it, we present results of computations of the spectral sequence. Based on these computations, we make a number of conjectures concerning the structure…

Calculates spectral flow bounds for reducible solutions to Vafa-Witten equations.

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.

The Khovanov homology of a link in $S^3$ and the Heegaard Floer homology of its branched double cover are related through a spectral sequence constructed by Ozsváth and Szabó. This spectral sequence has topological applications but is difficult to compute. We build an isomorphic spectral sequence whose underlying filte…

The paper explores the Rumin complex and spectral sequence on Carnot groups.

Researchers describe a spectral sequence for knots in 3D space.

This paper defines a spectral sequence connecting knot homologies.

New symplectic annular Khovanov homology connects knot theory to Floer homology.

Novel proof technique for Gelfand-Fuks cohomology.

We introduce three spectral sequences which give some expressions of colored Jones polynomials. Each spectral sequence contains a Khovanov-type homology groups. Two of them are derived from a bicomplex of the colored Jones polynomial. The other is the spectral sequence that deduces a colored Rasmussen invariant of link…

In this paper, we develop Leray-Serre-type spectral sequences to compute the intersection homology of the regular neighborhood and deleted regular neighborhood of the bottom stratum of a stratified PL-pseudomanifold. The E^2 terms of the spectral sequences are given by the homology of the bottom stratum with a local co…

In this paper we study the local description of spaces of forms on transitive Lie algebroids. We use this local description to introduce global structures like metrics, $\ast$-Hodge operation and integration along the algebraic part of the transitive Lie algebroid (its kernel). We construct a Čech-de Rham bicomplex wit…

The C-spectral sequence was introduced by Vinogradov in the late Seventies as a fundamental tool for the study of algebro-geometric properties of jet spaces and differential equations. A spectral sequence arise from the contact filtration of the modules of forms on jet spaces of a fibring (or on a differential equation…

Spectral sequence analysis for Sobolev mappings in Carnot groups.

We study the spectral functions, and in particular the zeta function, associated to a class of sequences of complex numbers, called of spectral type. We investigate the decomposability of the zeta function associated to a double sequence with respect to some simple sequence, and we provide a technique for obtaining the…

New Khovanov homology for links with multiple punctures.

Given a link in the three-sphere, Z. Szabó and the second author constructed a spectral sequence starting at the Khovanov homology of the link and converging to the Heegaard Floer homology of its branched double-cover. The aim of this paper and its sequel is to explicitly calculate this spectral sequence, using bordere…