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 higher genus polylogarithms under Riemann surface degenerations.
New proof for higher rank subvarieties in genus three.
New maxfaces with Enneper ends found.
For certain classes of knots we define geometric invariants called higher-order genera. Each of these invariants is a refinement of the slice genus of a knot. We find lower bounds for the higher-order genera in terms of certain von Neumann -invariants, which we call higher-order signatures. The higher-order genera o…
The study proves conditions for hyperbolic isometries on fine curve graphs of higher genus surfaces.
Paper shows string cobordism at 24 dims can be determined by elliptic genus.
We construct Weierstrass data for higher genus embedded doubly periodic minimal surfaces and present numerical evidence that the associated period problem can be solved. In the orthogonal ends case, there previously was only one known surface for each genus. We illustrate multiple new examples for each genus g>2. In th…
The study proves a geometric inequality for surfaces with genus G.
The paper defines and analyzes homotopic rotation sets for surfaces of higher genus.
We construct higher genus Riemann's minimal surfaces properly embedded in the Euclidean space. To do that we glue end by end a Costa-Hoffman-Meeks examples to two halves genus zero Riemann's minimal surfaces. In first we need to perform a deformation of a Costa-Hoffman-Meeks example to prescribe the flux vector along t…
Study on maximal surfaces with high genus in Lorentz-Minkowski space.
The abstract theorem is extended to higher genus surfaces.
We show that a torus knot which is not 2-bridge has a unique irreducible bridge splitting of positive genus.
Proves Alexander and Markov theorems for higher genus virtual doodles.
We define higher genus Gromov-Witten invariants and establish a mathematical theory of sigma model coupled with gravity over any semi-positive symplectic manifolds. As applications, we verify the stablizing conjecture of symplectic 4-manifolds for simply connected elliptic surfaces and construct smooth 6-manifolds admi…
We complete the classification of rank two affine manifolds in the moduli space of translation surfaces in genus three. Combined with a recent result of Mirzakhani and Wright, this completes the classification of higher rank affine manifolds in genus three.
Geodesic flows on certain surfaces are shown to be semi-conjugate to expansive flows.
Contact connected sums do not increase support genus.
New homotopy types defined for links in thickened surfaces with higher genus.
We construct an infinite family of homologous, non-isotopic, symplectic surfaces of any genus greater than one in a certain class of closed, simply connected, symplectic four-manifolds. Our construction is the first example of this phenomenon for surfaces of genus greater than one.
We formulate and solve the analog of the universal Conformal Ward Identity for the stress-energy tensor on a compact Riemann surface of genus , and present a rigorous invariant formulation of the chiral sector in the induced two-dimensional gravity on higher genus Riemann surfaces. Our construction of the action f…
In this note we study the topology of 3-dimensional initial data sets with horizons of a sort associated with asymptotically locally anti-de Sitter spacetimes. We show that, within this class, those initial data sets which contain no (immersed) marginally outer trapped surfaces in their interior must have simple topolo…
The paper studies right-angled links on higher genus surfaces.
For every odd natural number g=2d+1 we prove the existence of a countably infinite family of special Lagrangian cones in C^3 over a closed Riemann surface of genus g, using a geometric PDE gluing method.
Maps Heegaard Floer homology to Hecke algebras for surfaces.
It is known that knot Floer homology detects the genus and Alexander polynomial of a knot. We investigate whether knot Floer homology of detects more structure of minimal genus Seifert surfaces for . We define an invariant of algebraically slice, genus one knots and provide examples to show that knot Floer homol…
We show existence of constant mean curvature 1 surfaces in both hyperbolic 3-space and de Sitter 3-space with two complete embedded ends and any positive genus up to genus twenty. We also find another such family of surfaces in de Sitter 3-space, but with a different non-embedded end behavior.
In 1980 J. Powell proposed that five specific elements sufficed to generate the Goeritz group of any Heegaard splitting of , extending work of Goeritz on genus splittings. Here we prove that Powell's conjecture was correct for splittings of genus as well, and discuss a framework for deciding the truth of t…
An updated proof of a 1933 theorem of Goeritz, exhibiting a finite set of generators for the group of automorphisms of the 3-sphere that preserve a genus two Heegaard splitting. The group is analyzed via its action on a certain connected 2-complex. (The analogous problem for higher genus Heegaard splittings appears to …
New open books defy positive factorisation in genus one.
Researchers create projective representations of Hecke groups using TQFT.
Counting meanders on surfaces of arbitrary genus, with precise asymptotics.
We show that after one stabilization, a strongly irreducible Heegaard splitting of suitably large genus of a graph manifold is isotopic to an amalgamation along a modified version of the system of canonical tori in the JSJ decomposition. As a corollary, two strongly irreducible Heegaard splittings of a graph manifold o…
Derives formulas for determinant of Laplacian on curved surfaces.
This is the first of a series of two technical papers devoted to the analysis of holonomy invariants in strict higher gauge theory with end applications in higher Chern--Simons theory. For a flat 2--connection, we define the 2-holonomy of surface knots of arbitrary genus and determine its covariance properties under 1-…
Smooth HP^2 bundle over S^4 with nontrivial A-genus found.
The mathematical physicists Bershadsky-Cecotti-Ooguri-Vafa (BCOV) proposed, in a seminal article from '94, a conjecture extending genus zero mirror symmetry to higher genera. With a view towards a refined formulation of the Grothendieck-Riemann-Roch theorem, we offer a mathematical description of the BCOV conjecture at…
In previous work, the author fully classified orbit closures in genus three with maximally many (four) zero Lyapunov exponents of the Kontsevich-Zorich cocycle. In this paper, we prove that there are no higher dimensional orbit closures in genus three with any zero Lyapunov exponents. Furthermore, if a Teichmüller curv…
The study examines stable minimal surfaces in higher dimensions and provides bounds on their properties.
We define and study the signature, A-hat genus and higher signatures of the quotient space of an -action on a closed oriented manifold. We give applications to questions of positive scalar curvature and to an Equivariant Novikov Conjecture.
We construct integral bases for the SO(3)-TQFT-modules of surfaces in genus one and two at roots of unity of prime order and show that the corresponding mapping class group representations preserve a unimodular Hermitian form over a ring of algebraic integers. For higher genus surfaces the Hermitian form sometimes must…
Stable subgroups identified in genus two handlebody group.
This paper explains the conjectured algebraic duality between genus zero Gromov-Witten theory and genus zero "Closed String topology". This duality in another perspective is discussed on page 87 of the book "Frobenius manifold, quantum cohomology, and moduli spaces" (by Yuri Manin). This paper also discusses Fulton Mac…
Confirming the Powell Conjecture for genus-3 Heegaard splittings of the 3-sphere.
For large genus, precise monodromy groups are calculated for surface covers.
Constant mean curvature surfaces in can be studied via their associated family of flat connections. In the case of tori this approach has led to a deep understanding of the moduli space of all CMC tori. For compact CMC surfaces of higher genus the theory is far more involved due to the non abelian nature of their…
The paper constructs surfaces of high genus with three ends.
This is an informal set of lecture notes on moduli spaces of curves based on a set of lectures given at the ICTP last summer. It begins at an elementary level and discusses the genus 1 case in detail. The notes then give an informal treatement of Teichmuller space and higher genus moduli spaces. The point of view is ge…