arXiv research

New concordance invariant from spectral sequence on Khovanov homology.

Spectral sequence connects knot homologies to quotient knots.

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

We investigate the filtered theory corresponding to the universal sl(2) foam cohomology $H_{a,h}$ for links, where a and h are complex numbers. We show that there is a spectral sequence converging to $H_{a,h}$ which is invariant under the Reidemeister moves, and whose E1 term is isomorphic to Khovanov homology. This sp…

We define a family of link concordance invariants $\left\{ s_n \right\}_{n=2,3, \cdots}$. These link concordance invariants give lower bounds on the slice genus of a link $L$. We compute the slice genus of positive links. Moreover, these invariants give lower bounds on the link splitting number of a link. Especially, t…

Study improves understanding of Ricci curvature in manifolds.

New method for triclustering with reduced arbitrariness.

Improved SSD for faster and more accurate goodness-of-fit tests and model learning.

The abstract discusses a spectral sequence for Lie algebroids.

Introduces slice knots and concordance, linking to exotic smooth structures.

The unknotting number of a knot is bounded from below by its slice genus. It is a well-known fact that the genera and unknotting numbers of torus knots coincide. In this note we characterize quasipositive knots for which the genus bound is sharp: the slice genus of a quasipositive knot equals its unknotting number, if …

Spectral sequence connects knot homologies via algebraic geometry.

We realise Stroppel's extended arc algebra in the Fukaya-Seidel category of a natural Lefschetz fibration on the generic fiber of the adjoint quotient map on a type $A$ nilpotent slice with two Jordan blocks, and hence obtain a symplectic interpretation of certain parabolic two-block versions of Bernstein-Gelfan'd-Gelf…

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.

New invariants from framed instanton homology for knot concordance.

Cohomological and homological spectral sequences are shown to be isomorphic.

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

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

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…

Study of a $G_2$-equivariant octonionic operator and its right spectrum.

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…

Constructs Serre spectral sequence for bounded cohomology.

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.

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…

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

This paper defines a spectral sequence connecting knot homologies.

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

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…

We investigate the ramifications of the Legendrian satellite construction on the relation of Lagrangian cobordism between Legendrian knots. Under a simple hypothesis, we construct a Lagrangian concordance between two Legendrian satellites by stacking up a sequence of elementary cobordisms. This construction narrows the…

A new method optimizes slicing directions for SW distances to improve high-dimensional probability measure comparison.

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…

A knot in the 3-sphere is called doubly slice if it is a slice of an unknotted 2-sphere in the 4-sphere. We give a bi-sequence of new obstructions for a knot being doubly slice. We construct it following the idea of Cochran-Orr-Teichner's filtration of the classical knot concordance group. This yields a bi-filtration o…

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…

Combining known spectral sequences with a new spectral sequence relating reduced and unreduced sl(N)-homology yields a relationship between the Homflypt-homology of a knot and its sl(N)-concordance invariants. As an application, some of the sl(N)-concordance invariants are shown to be linearly independent.

Develops a spectral sequence for Lie group actions on manifolds.

New spectral sequences define knot invariants.

We introduce and study a new spectral sequence associated with a Poisson group action on a Poisson manifold and an equivariant momentum mapping. This spectral sequence is a Poisson analog of the Leray spectral sequence of a fibration. The spectral sequence converges to the Poisson cohomology of the manifold and has the…

Given a link in the three-sphere, Ozsváth and Szabó showed that there is 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 is to explicitly calculate this spectral sequence in terms of bordered Floer homolo…

There are a number of homological knot invariants, each satisfying an unoriented skein exact sequence, which can be realized as the limit page of a spectral sequence starting at a version of the Khovanov chain complex. Compositions of elementary 1-handle movie moves induce a morphism of spectral sequences. These morphi…

A spectral sequence is established, whose $E_{2}$ page is Bar-Natan's variant of Khovanov homology and which abuts to a deformation of instanton homology for knots and links. This spectral sequence arises as a specialization of a spectral sequence whose $E_{2}$ page is a characteristic-2 version of $F_{5}$ homology, in…

Extends Khovanov homology spectral sequence using Heegaard Floer homology.