Lobb observed in [arXiv:1103.1412] that each equivariant sl(N) Khovanov-Rozansky homology over C[a] admits a standard decomposition of a simple form. In the present paper, we derive a formula for the corresponding Lee-Gornik spectral sequence in terms of this decomposition. Based on this formula, we give a simple alter…
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48 results for “Lee spectral sequence”
We show that the page at which the Lee spectral sequence collapses gives a bound on the unknotting number, u(K). In particular, for knots with u(K)<3, we show that the Lee spectral sequence must collapse at the E_2 page. An immediate corollary is that the Knight Move Conjecture is true when u(K)<3.
Calculates knot -torsion order using spectral sequences.
problem Calculating the -torsion order of knots.
method Using the reduced Bar-Natan--Lee--Turner spectral sequence.
result Example of -torsion order .
Counterexample disproves Knight Move Conjecture.
problem Disproving the Knight Move Conjecture for knots.
method Presented a counterexample with a specific knot.
result Found a knot where Lee spectral sequence has a nontrivial differential of bidegree (1,8).
New concordance invariant from spectral sequence on Khovanov homology.
problem Concordance invariants from spectral sequences.
method Constructing from spectral sequence on Khovanov homology.
result Provides a bound on the nonorientable slice genus.
Some link homologies in math.GT
New link homology theories for yield distinct invariants.
problem Extending link homologies for links in .
method Introducing new Lee and Bar-Natan spectral sequences for links in .
result New Lee and Bar-Natan invariants are distinct from existing ones.
Developed a new homology theory for graph chromatic polynomials.
problem Categorification of chromatic polynomials.
method Introduced a new homology theory and developed a spectral sequence.
result Spectral sequence converges to , supporting .
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…
Based on the results of the second author, we define an equivariant version of Lee and Bar-Natan homology for periodic links and show that there exists an equivariant spectral sequence from the equivariant Khovanov homology to equivariant Lee homology. As a result we obtain new obstructions for a link to be periodic. T…
New algorithm calculates -invariants for links efficiently.
problem Cannot be done by standard spectral sequence methods.
method Developed an algorithm for -invariants of links.
result Demonstrated efficiency and applicability to sl(3)-link homology.
The paper extends Khovanov homology results to homologies and provides bounds on knot properties.
problem Extending Khovanov homology results to homologies and knot properties.
method Spectral sequence arguments and Levine-Zemke's ribbon concordance obstruction.
result Bounds on the alternation number and Turaev genus of knots.
We use a special kind of 2-dimensional extended Topological Quantum Field Theories (TQFTs), so-called open-closed TQFTs, in order to extend Khovanov homology from links to arbitrary tangles, not necessarily even. For every plane diagram of an oriented tangle, we construct a chain complex whose homology is invariant und…
We introduce the notion of a Khovanov-Floer theory. Roughly, such a theory assigns a filtered chain complex over Z/2 to a link diagram such that (1) the E_2 page of the resulting spectral sequence is naturally isomorphic to the Khovanov homology of the link; (2) this filtered complex behaves nicely under planar isotopy…
We construct an equivariant colored sl(N)-homology for links, which generalizes both the colored sl(N)-homology defined by the author and the equivariant sl(N)-homology defined by Krasner. The construction is a straightforward generalization of that of the colored sl(N)-homology. The proof of invariance is based on a s…
Proves Khovanov homology conjecture for 3-stranded braids.
problem Khovanov homology of 3-stranded braid closures.
method Bar-Natan's version of Khovanov homology for tangles, delooping, cancellation techniques, and spectral sequences.
result Khovanov homology of 3-stranded braid closures contains only 2-torsion.
We provide a unified framework for proving Reidemeister-invariance and functoriality for a wide range of link homology theories. These include Lee homology, Heegaard Floer homology of branched double covers, singular instanton homology, and \Szabo's geometric link homology theory. We follow Baldwin, Hedden, and Lobb (a…
We prove that every H-thin link has no -torsion for in its Khovanov homology. Together with previous results by Eun Soo Lee and the author, this implies that integer Khovanov homology of non-split alternating links is completely determined by the Jones polynomial and signature. Our proof is bas…
The paper classifies links with low rank knot Floer and Khovanov homologies.
problem Detecting and classifying links with low rank knot Floer and Khovanov homologies.
method Generalized link Floer homology, used to obtain rank bounds and classify links.
result Knot Floer homology detects and .
Lee's work on twisted torus knots with Fibonacci parameters is extended to Horadam parameters.
problem Classifying twisted torus knots with Horadam parameters.
method Using recursive Horadam parameters to generalize Lee's work on Fibonacci parameters.
result Families of twisted torus knots with Horadam parameters are provided.
The abstract discusses a spectral sequence for Lie algebroids.
problem The abstract tackles the spectral sequence of Lie algebroids.
method The abstract presents a spectral sequence for Lie algebroids, generalizing classical constructions.
result The spectral sequence converges to Lie algebroid cohomology for wide Lie subalgebroids and to formal Lie algebroid cohomology for Lie subalgebroids over proper submanifolds.
Oeljeklaus-Toma (OT) manifolds are complex non-Kähler manifolds whose construction arises from specific number fields. In this note, we compute their de Rham cohomology in terms of invariants associated to the background number field. This is done by two distinct approaches, one using invariant cohomology and the other…
We formulate a more conceptual interpretation of the Cappell-Lee-Miller glueing/splitting theorem using the new language of asymptotic maps and asymptotic exactness. Additionally, we present an asymptotic description of the Mayer-Vietoris sequence naturally associated to the Cech cohomology of the sheaf of local soluti…
Study on spectral sequence of Iwasawa manifold and its deformations.
problem Properties of Frölicher spectral sequence on Iwasawa manifold and its deformations.
method Determination of successive pages of the Frölicher spectral sequence.
result New examples and counterexamples on spectral sequence properties.
Spectral sequence connects knot homologies via algebraic geometry.
problem Connecting algebraic and geometric knot homologies.
method Bigraded spectral sequence from gl(0)-homology to knot Floer homology.
result Constructs a Bockstein-type spectral sequence.
Incompatible operations affect Khovanov homology and spectral sequences.
problem Incompatibility between operations and spectral sequences.
method Observation of obstructions to integral lifting and spectrification.
result Lipshitz-Sarkar Steenrod operations are incompatible with Szabo's spectral sequence.
The spectral sequence's -page is a link invariant for .
problem Proving the invariance of the spectral sequence pages.
method Analyzing the spectral sequence construction and its properties.
result The -page is a link invariant for .
The paper explores spectral sequences of complex manifolds with special metrics.
problem Understanding spectral sequences of compact complex manifolds with special metrics.
method Investigation of Frölicher spectral sequences and special metrics (balanced, SKT, Gauduchon) on manifolds.
result Found compact manifolds where spectral sequences do not degenerate at the second page, providing counterexamples and new families.
Cohomological and homological spectral sequences are shown to be isomorphic.
problem Cohomological and homological Atiyah-Hirzebruch spectral sequences are not always isomorphic.
method Spanier-Whitehead duality is used to establish an isomorphism between the two spectral sequences.
result Cohomological and homological Atiyah-Hirzebruch spectral sequences are isomorphic for finite spectra.
Establishes a spectral sequence linking instanton and Khovanov homologies.
problem Connecting instanton and Khovanov homologies.
method Develops a spectral sequence specializing invariants from characteristic-2 homology.
result A spectral sequence connects instanton and Khovanov homologies.
Describes the relationship between two spectral sequences and their joint refinement.
problem Computing the cohomology of a group or space using spectral sequences.
method Joint tri-graded refinement of the Leray--Serre and Eilenberg--Moore spectral sequences.
result One of the spectral sequences always degenerates from its second page, and the other satisfies a local-to-global property.
Defines spectral sequences for fiberwise Dirac operators and proves adiabatic limit formula.
problem Calculating eta invariants for fibrations.
method Heat kernel method and analytic localization techniques.
result Extends remainder terms of eta invariants in fibrations.
Spectral sequence connects knot homologies to quotient knots.
problem Distinguishing knots using homology.
method Construct spectral sequence relating Khovanov homology to quotient knots.
result Khovanov homology distinguishes certain slice disks.
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.
problem No specific problem stated; focuses on a new mathematical construction.
method Constructs the Serre spectral sequence for bounded cohomology.
result Obtains a non-isometric generalization of Gromov's mapping theorem and partial results on simplicial volume.
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 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.
problem Understanding the relationship between Rumin complex and spectral sequence on Carnot groups.
method Investigates the Rumin complex and spectral sequence on Carnot groups, focusing on the filtration by homogeneous weights.
result Provides a detailed insight into the relationship between the Rumin complex and the 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…
The paper bounds higher Steklov eigenvalues of graphs on surfaces.
problem Bounding higher Steklov eigenvalues of graphs on surfaces.
method Using metrical deformation via probability flows, the upper bound is derived.
result The upper bound of higher Steklov eigenvalues is established.
Researchers describe a spectral sequence for knots in 3D space.
problem Understanding the Sinha spectral sequence for knots in R^3.
method Explicit description using Fox Neuwirth chain complexes and multicomplex structure.
result A non-trivial third page differential found, contradicting the rational case.
This paper defines a spectral sequence connecting knot homologies.
problem Link Floer homology and its connections to knot homologies.
method Iterating a modified skein exact triangle to create a spectral sequence.
result A spectral sequence from reduced Khovanov homology of the mirror of a knot to knot Floer homology of the knot.
Study on spectral sequence for abelian Lie group actions, with bounds and applications.
problem Understanding the spectral sequence for abelian Lie group actions.
method Provided upper bounds and examples to show these bounds are sharp.
result Sharp bounds on the degeneration page of spectral sequence.
Spectral sequences of colored Jones polynomials, colored Rasmussen invariants and nanophrasesmath.GT
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…
The main goal of the present paper is to construct new invariants of knots with additional structure by adding new gradings to the Khovanov complex. The ideas given below work in the case of virtual knots, closed braids and some other cases of knots with additional structure. The source of our additional grading may be…
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.
problem Analyzing spectral sequences for Sobolev mappings in Carnot groups.
method Showed Pansu pullback induces a spectral sequence mapping.
result Pansu pullback induces a spectral sequence mapping.
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.
problem Defining a new Khovanov homology for links with multiple punctures.
method Defined a variant of Khovanov homology for links in thickened disks with multiple punctures, related to previous work by spectral sequences.
result Spectral sequences recover annular Khovanov homology to Khovanov homology.