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.
Researchers found the second homology of Torelli groups for large g.
We determine the second homology group of the homological Goldman Lie algebra for an oriented surface.
This paper computes the second quandle homology group of knot n-quandles.
Study shows rank of knot Floer homology detects Hopf links and classifies second smallest links.
We define a map from second quandle homology to the Schur multiplier and examine its properties. Furthermore, we express the second homology of Alexander quandles in terms of exterior algebras. Additionally, we present a self-contained proof of its structure and provide some computational examples.
We develop a theory of equivariant group presentations and relate them to the second homology group of a group. Our main application says that the second homology group of the Torelli subgroup of the mapping class group is finitely generated as an -module.
Torelli group's second homology is finite for large genus surfaces.
Proposes a method to compute the second Steenrod square for odd Khovanov homology.
Study on planar graph braid groups' second homology.
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…
Computes second homology groups of orbifold groups, proving profinite rigidity and Grothendieck pairs.
In this paper, we generalize the work of the second author and prove a grading shifting property, in sutured monopole and instanton Floer theories, for general balanced sutured manifolds. This result has a few consequences. First, we offer an algorithm that computes the Floer homologies of a family of sutured handle-bo…
Investigates minimal genus of second homology classes in RAAGs, finding bounds and specific cases.
Paper proves vanishing homology groups for certain hyperbolic groups.
This is the fourth of five papers that construct an isomorphism between the Seiberg-Witten Floer homology and the Heegaard Floer homology of a given compact, oriented 3-manifold. The isomorphism is given as a composition of three isomorphisms; the first of these relates a version of embedded contact homology on an an a…
We prove that if G is an abelian group of odd order then there is an isomorphism from the second quandle homology of the Takasaki quandle of G to the exterior square of G. In particular, for G=Z_k^n, k odd, we obtain Z_k^{n(n-1)/2}. Nontrivial second homology allows us to use 2-cocycles to construct new quandles from T…
Study initiates homology theory for Bol-Moufang quasigroups.
We prove a representation stability result for the second homology groups of Torelli subgroups of mapping class groups and automorphism groups of free groups. This strengthens the results of Boldsen-Hauge Dollerup and Day-Putman. We also prove a new representation stability result for the homology of certain congruence…
We study the Thurston norm on the second homology of a 3-manifold M, which is the surface bundle over the circle with a pseudo-Anosov monodromy. A novelty of our approach consists in the application of the C*-algebras to a problem in topology. Namely, one associates to M a C*-algebra, whose K-theory gives rise to an al…
We focus on two kinds of infinite index subgroups of the mapping class group of a surface associated with a Lagrangian submodule of the first homology of a surface. These subgroups, called Lagrangian mapping class groups, are known to play important roles in the interaction between the mapping class group and finite-ty…
We show that monopole Floer homology (as defined by Kronheimer and Mrowka) is isomorphic to the S^1-equivariant homology of the Seiberg-Witten Floer spectrum constructed by the second author.
Researchers find a Steenrod square for link Floer homology.
By calculating the Fermat limit of certain q-Fermat functions, we get explicit surgery formulae for the second and third Ohtsuki invariants for homology 3-spheres. The surgery formula of the second Ohtsuki invariant λ_2, combined with an argument using the general theory of finite type invariants of homology 3-spheres,…
In this survey paper, we give a complete list of known results on the first and the second homology groups of surface mapping class groups. Some known results on higher (co)homology are also mentioned.
Researchers determined the second homology group of a specific symplectic derivation Lie algebra.
Study instanton Floer homology for links in RP^3 and use it to detect knots.
We prove a basic inequality for the d-invariants of a splice of knots in homology spheres. As a result, we are able to prove a new relation on the rank of reduced Floer homology under maps between Seifert fibered homology spheres, improving results of the first and second authors. As a corollary, a degree one map betwe…
Adjusts Yang-Baxter operators for HOMFLYPT polynomials.
Survey of bordered Floer homology for 3-manifolds with boundary.
New examples show not all homology fiber bundles are topological.
Computes quandle associated groups using group homology.
New interpretation of Mayer-Vietoris sequence using überhomology.
In this paper, we introduce the annular instanton Floer homology which is defined for links in a thickened annulus. It is an analogue of the annular Khovanov homology. A spectral sequence whose second page is the annular Khovanov homology and which converges to the annular instanton Floer homology is constructed. As an…
We define a second Steenrod square for virtual links, which is stronger than Khovanov homology for virtual links, toward constructing Khovanov-Lipshitz-Sarkar stable homotopy type for virtual links. This induces the first meaningful nontrivial example of the second Steenrod square operator on the Khovanov homology for …
Paper constructs a spectral sequence linking annular Khovanov homology to reduced Khovanov homology.
Paper computes a specific term of knot homology for 3-braids.
Study on homology groups of cDV singularity links, identifying their topology.
Study pinched submanifolds, proving homology vanishing results.
Study homology groups of mapping and Torelli groups for surfaces with abelian covers.
The based loop space homology of a special family of homogeneous spaces, flag manifolds of connected compact Lie groups is studied. First, the rational homology of the based loop space on a complete flag manifold is calculated together with its Pontrjagin structure. Second, it is shown that the integral homology of the…
Authors compute stable homology of torus knots using a new deformation technique.
Study HOMFLY-PT homology structure for knots up to 11 crossings.
We define the universal sl3-link homology, which depends on 3 parameters, following Khovanov's approach with foams. We show that this 3-parameter link homology, when taken with complex coefficients, can be divided into 3 isomorphism classes. The first class is the one to which Khovanov's original sl3-link homology belo…
Let M be an arithmetic hyperbolic 3-manifold, such as a Bianchi manifold. We conjecture that there is a basis for the second homology of M, where each basis element is represented by a surface of `low' genus, and give evidence for this. We explain the relationship between this conjecture and the study of torsion homolo…
Invariants for 3-manifolds with toral boundaries, related by sutured decompositions.
Let denote the group of knots in homology spheres that bound homology balls, modulo smooth concordance in homology cobordisms. Answering a question of Matsumoto, the second author previously showed that the natural map from the smooth knot concordance group to $\wideha…
This article is a standalone introduction to sutured Floer homology for graduate students in geometry and topology. It is divided into three parts. The first part is an introductory level exposition of Lagrangian Floer homology. The second part is a construction of Heegaard Floer homology as a special, and slightly mod…
As Oleg Viro describes in his paper, the most fundamental property of the Khovanov homology group is their invariance under Reidemeister moves. Viro constructes Khovanov complex and homology consisting of Jordan curves with sign and also gives a proof for the only case of first Reidemeister move by using his definition…