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.
Study supports conjecture about pretzel links' homology.
The paper studies knot Floer homology under Murasugi sum and establishes graded isomorphisms.
We consider various homological operations on homology of quandles. We introduce the notion of quandle partial derivatives, and extreme chains on which appropriate partial derivatives vanish. Extreme chains yield homological operations. We also consider the degree one homology operations created using elements of the q…
Proves Khovanov homology has no torsion for bipartite circle graphs.
Sharp upper bound for quasi polynomial degree of manifold configuration spaces.
It was proven by González-Meneses, Manchón and Silvero that the extreme Khovanov homology of a link diagram is isomorphic to the reduced (co)homology of the independence simplicial complex obtained from a bipartite circle graph constructed from the diagram. In this paper we conjecture that this simplicial complex is al…
Knot Floer homology stabilizes with twists.
We introduce the notion of partial presimplicial set and construct its geometric realization. We show that any semiadequate diagram yields a partial presimplicial set leading to a geometric realization of the almost-extreme Khovanov homology of the diagram. We give a concrete formula for the homotopy type of this geome…
This paper defines girth for knots and links, linking it to Khovanov homology.
The study examines how twisting a knot affects its homology and stability properties.
We extend Perutz's Lagrangian matching invariants to 3-manifolds which are not necessarily fibred using the technology of holomorphic quilts. We prove an isomorphism of these invariants with Ozsvath-Szabo's Heegaard Floer invariants for certain extremal spin^c structures. As applications, we give new calculations of He…
Circle graph complexes reveal link properties via Khovanov homology.
We prove twisted homological stability with polynomial coefficients for automorphism groups of free nilpotent groups of any given class. These groups interpolate between two extremes for which homological stability was known before, the general linear groups over the integers and the automorphism groups of free groups.…
We show that the action of the mapping class group on bordered Floer homology in the second to extremal spin^c-structure is faithful. This paper is designed partly as an introduction to the subject, and much of it should be readable without a background in Floer homology.
The Turaev genus of a link can be thought of as a way of measuring how non-alternating a link is. A link is Turaev genus zero if and only if it is alternating, and in this viewpoint, links with large Turaev genus are very non-alternating. In this paper, we study Turaev genus one links, a class of links which includes a…
We give a systematic method to calculate some homological data from the global monodromy of a topological elliptic surface. We apply this method to the cases 1) the transcendental lattice of an extremal elliptic K3 surface, 2) the torsion part of Mordell-Weil group of a general elliptic surface, and 3) the Mordell-Weil…
We study the Sasaki cone of a CR structure of Sasaki type on a given closed manifold. We introduce an energy functional over the cone, and use its critical points to single out the strongly extremal Reeb vectors fields. Should one such vector field be a member of the extremal set, the scalar curvature of a Sasaki extre…
I use local differential geometric techniques to prove that the algebraic cycles in certain extremal homology classes in Hermitian symmetric spaces are either rigid (i.e., deformable only by ambient motions) or quasi-rigid (roughly speaking, foliated by rigid subvarieties in a nontrivial way). These rigidity results ha…
In previous work, we have constructed diagrammatic idempotents in an affine extension of the Temperley-Lieb category, which describe extremal weight projectors for sl(2), and which categorify Chebyshev polynomials of the first kind. In this paper, we generalize the construction of extremal weight projectors to the case…
Develops a new spectrum for annular links, recovering a transverse invariant at extreme gradings.
Study detects a specific type of link using annular Khovanov homology.
The paper proves properties of strata of differentials, showing they are affine and extremal.
This paper explores Khovanov adequacy in knot theory.
Investigates dual foliations of polygon spaces based on area and perimeter.
New examples show Sasaki manifolds without extremal metrics.
We prove that a Lefschetz fibration over the disc that, after compactification, has the same singular fibers as an extremal rational elliptic surface can be obtained by deleting a singular fiber and a section from the rational extremal elliptic surface, i.e. such a Lefschetz fibration is determined up to topological eq…
Study Khovanov homology of Turaev genus one links, finding a trivial summand.
Using the Sasakian join construction with homology 3-spheres, we give a countably infinite number of examples of Sasakian manifolds with perfect fundamental group in all odd dimensions greater than 1. These have extremal Sasaki metrics with constant scalar curvature. Moreover, we present further examples of both Sasaki…
The paper finds CSC Sasaki metrics on specific 7-manifolds.
We present some enumerative and structural results for flag homology spheres. For a flag homology sphere , we show that its -vector satisfies: \begin{align*} γ_j=0,\text{ for all } j>γ_1, \quad γ_2\leq\binom{γ_1}{2}, \quad γ_{γ_1}\in\{0,1\}, \quad \text{ and }γ_{γ_1-1}\in\{0,1,2,γ_1\}, \e…
We show that for a generic nullhomotopic simple closed curve C in the boundary of a compact, orientable, mean convex 3-manifold M with trivial second homology, there is a unique area minimizing disk D embedded in M where the boundary of D is C. We also show that the same is true for absolutely area minimizing surfaces.
New homology theory for graphs detects subdivisions and homology manifolds.
PHINN: A generative model for rare-event time series using persistent homology
In this article, we introduce a fixed parameter tractable algorithm for computing the Turaev-Viro invariants TV(4,q), using the dimension of the first homology group of the manifold as parameter. This is, to our knowledge, the first parameterised algorithm in computational 3-manifold topology using a topological parame…
The closed string field theory minimal-area problem asks for the conformal metric of least area on a Riemann surface with the condition that all non-contractible closed curves have length at least 2π. This is an extremal length problem in conformal geometry as well as a problem in systolic geometry. We consider the ana…
New insights into Khovanov homology complexity and topological structure.
For an oriented irreducible 3-manifold M with non-empty toroidal boundary, we describe how sutured Floer homology () can be used to determine all fibered classes in . Furthermore, we show that the of a balanced sutured manifold detects which classes in admit a taut depth one foliatio…
In this paper we study the Lie groupoids which appear in foliation theory. A foliation groupoid is a Lie groupoid which integrates a foliation, or, equivalently, whose anchor map is injective. The first theorem shows that, for a Lie groupoid G, the following are equivalent: - G is a foliation groupoid, - G has discrete…
In this paper, we investigate the topology of a class of non-Kähler compact complex manifolds generalizing that of Hopf and Calabi-Eckmann manifolds. These manifolds are diffeomorphic to special systems of real quadrics in which are invariant with respect to the natural action of the real torus $(\Bbb S^1)^n…
Let G be a connected bipartite graph with color classes E and V and root polytope Q. Regarding the hypergraph (V,E) induced by G, we prove that its interior polynomial is equivalent to the Ehrhart polynomial of Q, which in turn is equivalent to the h-vector of any triangulation of Q. It follows that the interior polyno…
Study reveals failure of uniqueness in dynamical invariants for 3D volume-preserving diffeomorphisms.
New method uses Chern-Simons filtration to study corks and bounding.
ExGAN generates realistic extreme samples using GANs and EVT.
Study on extremals in sub-Lorentzian geometry defined by antinorm.
Study models extreme skew surges along French Atlantic coast.
Blowups of Kähler manifolds can inherit extremal metrics.
New approach to extremal hyperbolic surfaces using NEC groups.
Paper develops a novel approach to identify clusters of features in multivariate extremes.