A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
New construction of Fukaya-Seidel categories using complex gradient flow equation.
Seidel and Smith introduced the graded fixed-point symplectic Khovanov cohomology group Kh_{symp,inv}(K) for a knot K inside S^{3}, as well as a spectral sequence converging to the Heegaard Floer homology-hat group for the connected sum of the double branched cover with a copy of S^{2}xS^{1}. The E^{1}-page of this spe…
In 2001, Khovanov and Seidel constructed a faithful action of the (m+1)-strand braid group on the derived category of left modules over a quiver algebra, A_m. We interpret the Hochschild homology of the Khovanov-Seidel braid invariant as a direct summand of the sutured Khovanov homology of the annular braid closure.
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…
The paper calculates quantum cohomology for coadjoint orbits and Hamiltonian groups.
Let be an exact symplectic manifold equal to a symplectization near infinity and having stably trivializable tangent bundle, and be an exact symplectomorphism of which, near infinity, is equal to either the identity or the symplectization of a contactomorphism such that neither nor …
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 nilpotent slice with two Jordan blocks, and hence obtain a symplectic interpretation of certain parabolic two-block versions of Bernstein-Gelfan'd-Gelf…
Given a knot K in S^3, Seidel and Smith described in arXiv:1002.2648v3 a graded cohomology group Kh_{symp,inv}(K), a variant of their symplectic Khovanov cohomology group. They also constructed a spectral sequence converging to the Heegaard Floer-hat homology group for the connected sum of the double branched cover and…
We prove that a positive allowable Lefschetz fibration, PALF in short, admits a structure of exact Lefschetz fibration in the sense of Seidel \cite{Se08}. If the two-fold first Chern class of the total space is zero, we obtain the Fukaya-Seidel category. We prove that the derived Fukaya-Seidel category of PALF is indep…
We encode the variation structure of a quasihomogeneous polynomial with an isolated singularity as introduced by Nemethi in a set of spectral flows of the signature operator on the Milnor bundle by varying global elliptic boundary conditions in a specific way using the quasihomogeneous circle action on the Brieskorn la…
Given a J-holomorphic Morse function on a symplectic manifold, a new construction of the Fukaya-Seidel category is outlined. Applying this construction in an infinite dimensional case, a Fukaya-Seidel-type category is associated to a smooth three-manifold. In this case the construction is based on a five-dimensional ga…
We investigate a relationship between Ozsváth and Szabó's bordered theory and the algebras and bimodules constructed by Khovanov-Seidel. Specifically, we show that (a variant of) a special case of Ozsváth-Szabó's algebras has a quotient which is isomorphic to the Khovanov-Seidel quiver algebra with coefficients in $\ma…
We prove, in the case of hyperbolic 3-space, a couple of conjectures raised by J. J. Seidel in "On the volume of a hyperbolic simplex", Stud. Sci. Math. Hung. 21, 243-249, 1986. These conjectures concern expressing the volume of an ideal hyperbolic tetrahedron as a monotonic function of algebraic maps. More precisely, …
The abstract discusses a spectral sequence for Lie algebroids.
Given two Lagrangian spheres in an exact symplectic manifold, we find conditions under which the Dehn twists about them generate a free non-abelian subgroup of the symplectic mapping class group. This extends a result of Ishida for Riemann surfaces. The proof generalises the categorical version of Seidel's long exact s…
Study Dehn-Seidel twists on Lagrangian spheres in K3 surfaces.
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 -page is a link invariant for .
The paper explores spectral sequences of complex manifolds with special metrics.
Cohomological and homological spectral sequences are shown to be isomorphic.
Describes the relationship between two spectral sequences and their joint refinement.
Defines spectral sequences for fiberwise Dirac operators and proves adiabatic limit formula.
Spectral sequence connects knot homologies to quotient knots.
We discuss a relationship between Khovanov- and Heegaard Floer-type homology theories for braids. Explicitly, we define a filtration on the bordered Heegaard-Floer homology bimodule associated to the double-branched cover of a braid and show that its associated graded bimodule is equivalent to a similar bimodule define…
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 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…
Recent years have witnessed the rapid development of block coordinate update (BCU) methods, which are particularly suitable for problems involving large-sized data and/or variables. In optimization, BCU first appears as the coordinate descent method that works well for smooth problems or those with separable nonsmooth …
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…
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…
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…