On-device research index

arXiv research

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.

168,657 papers · 148 categories

Trend · papers per month

count % of corpus

9 results for “slice-torus”

On the values taken by slice torus invariantsmath.GT

Characterizes values of slice-torus invariants related to knot genus.

problem Understanding the values of slice-torus invariants for knots.

method Characterization based on stable smooth slice genus.

result Existence of slice torus invariants without explicit constructions.

slice-torus invariants knot genus stable smooth slice genus local Thom conjecture

2022-02-28abs ↗pdf ↗

An unoriented analogue of slice-torus invariantmath.GT

New invariant defined for unoriented knots, proving no factorization through topological concordance.

problem Defining and proving properties of unoriented slice-torus invariants.

method Introducing and proving properties of unoriented slice-torus invariants.

result Unoriented slice-torus invariants do not factor through the topological concordance group.

slice-torus invariant unoriented knot topological concordance knot concordance group 4-genus

2024-04-05abs ↗pdf ↗

Slice-torus concordance invariants and Whitehead doubles of linksmath.GT

In the present paper we extend the definition of slice-torus invariant to links. We prove a few properties of the newly-defined slice-torus link invariants: the behaviour under crossing change, a slice genus bound, an obstruction to strong sliceness, and a combinatorial bound. Furthermore, we provide an application to …

2018-06-27abs ↗pdf ↗

On the slice-torus invariant

q_M

from

\mathbb{Z}_2

-equivariant Seiberg--Witten Floer cohomologymath.GT

Abstract invariant cannot be expressed using various slice-torus invariants.

problem Cannot express Iida-Taniguchi's slice-torus invariant using other known invariants.

method Analysis of various known invariants and their properties.

result Iida-Taniguchi's slice-torus invariant cannot be realized as a linear combination of other invariants.

slice-torus invariant invariants Rasmussen's invariant Ozsváth-Szabó's invariant instanton invariant

2025-01-14abs ↗pdf ↗

A family of slice-torus invariants from the divisibility of Lee classesmath.GT

New invariants from divisibility of Lee classes for slice-torus.

problem Determining slice-torus knots using Lee class divisibility.

method Defined new invariants from divisibility of reduced Lee class invariants.

result New invariants coincide with Rasmussen invariant for certain cases.

slice-torus Lee class Khovanov homology invariant divisibility

2022-11-04abs ↗pdf ↗

Bennequin-Plamenevskaya-Shumakovitch type inequalities for Kronheimer-Mrowka's concordance invariantmath.GT

Lower bounds for a knot invariant are derived using computations and cobordism inequality.

problem Calculating the concordance invariant

s^{\#}

for knots.

method Computation for torus knots, cobordism inequality of

s^{\#}

, and arguments for slice-torus invariants.

result Lower bounds for

s^{\#}

are derived for knots.

knot theory concordance invariant torus knots cobordism slice-torus

2023-09-01abs ↗pdf ↗

A Refinement of the Spanning Surface Defect in

3

and

4

Dimensionsmath.GT

Refines knot defect measurement in 3D and 4D.

problem Measuring how far knots are from being alternating.

method Extends spanning surface defect to 4-ball, making comparisons and proving formulas.

result Connected sum formula proven.

knot theory spanning surfaces 3D 4D non-orientable

2026-02-13abs ↗pdf ↗

Monopoles and transverse knotsmath.GT

Study transverse knots and symplectic surfaces using Seiberg-Witten monopole equations.

problem Investigate transverse knots and symplectic surfaces via Seiberg-Witten monopole equations.

method Equivariant Seiberg-Witten theory on branched covers, introducing a novel slice-torus invariant.

result Determine the value of slice-torus invariant for certain Montesinos knots within a deviation of 2.

transverse knots symplectic surfaces Seiberg-Witten monopole equivariant theory slice-torus invariant

2024-03-23abs ↗pdf ↗

Slice-torus link invariants, combinatorial invariants, and positivity conditionsmath.GT

The study establishes conditions for positive and quasi-positive links.

problem Characterizing and testing positive and quasi-positive links.

method Proves necessary conditions for link concordance and positivity.

result Characterizes positive links with unlinking number 1 and 2, and tests positive links as closures of positive braids.

link theory positive links quasi-positive links concordance braid closure

2020-08-16abs ↗pdf ↗