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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

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← all fields·9 papers on “knot theory” in Geometric Topology · 1 month

A combinatorial approach to obstructing left-orderability of Dehn fillingsmath.GT

New property helps show many knot fillings are not left-orderable.

problem Non-left-orderability of knot groups after Dehn filling.

method Introducing conjugate-slope property to study knot groups.

result The conjugate-slope property implies non-left-orderability of many knot fillings.

knot theory Dehn filling left-orderability fundamental group meridian

2026-07-17abs ↗pdf ↗

Knotted surfaces with simply-connected complementsmath.GT

Study knotted surfaces in simply-connected 4-manifolds with trivial boundary.

problem Locally flat, compact, genus g surfaces with boundary a fixed knot in simply-connected 4-manifolds with boundary the 3-sphere.

method Analyzes homology and isotopy of surfaces with trivial fundamental group complements.

result Homologous surfaces are topologically ambiently isotopic rel. boundary.

knot theory 4-manifolds fundamental group ambient isotopy homology

2026-07-16abs ↗pdf ↗

fkcompute: an efficient

F_K

invariant calculatormath.GT

fkcompute calculates a knot invariant from a braid presentation.

problem Computing the Gukov-Manolescu invariant for complex knots and links.

method Three-phase pipeline: braid presentation search, state space encoding, R-matrix multiplication.

result fkcompute efficiently computes the invariant for knots and links up to 12 crossings.

knot theory invariant calculation braid presentation polytope R-matrices

2026-07-13abs ↗pdf ↗

Probabilistic pseudo knot theorymath.GT

Probabilistic pseudo knots model uncertain knot diagrams.

problem Modeling knots with unresolved crossings.

method Assign probabilities to undetermined crossings; define probabilistic equivalence and extend classical knot invariants.

result Capture uncertainty in physical, biological, and computational contexts.

knot theory probabilistic models uncertainty crossings 3-manifolds

2026-07-09abs ↗pdf ↗

Equivariant Grid Homology for Strongly Invertible Knotsmath.GT

Develops equivariant grid homology for strongly invertible knots.

problem Invariants of strongly invertible knots.

method Equivariant grid diagrams and mapping cones.

result Equivariant unknotting numbers and genus bounds.

knot theory equivariant homology strongly invertible knots grid diagrams invariants

2026-07-05abs ↗pdf ↗

Algebraic and Geometric Aspects of Non-Classical Knotsmath.GT

Survey of various non-classical knot theories from geometric and algebraic perspectives.

problem Various modifications to classical knot theory.

method Comparative geometric and algebraic analysis of non-classical knot theories.

result Distinct topological and combinatorial features in generalized knot theories.

knot theory non-classical knots skein modules three-manifolds pseudo knots

2026-07-05abs ↗pdf ↗

Permutation Jones Polynomialsmath.GT

A new knot invariant uses permutations to extend Jones polynomials.

problem Extending Jones polynomials to classical and virtual knots and links.

method Colorings by permutations of a finite set to define new knot invariants.

result Established properties and computed polynomials for small cases.

Jones polynomial permutations knot theory virtual knots

2026-07-01abs ↗pdf ↗

Deeply Slice Knot Detection via Immersed Curvesmath.GT

The paper tackles deeply slice knots via immersed curves.

problem Whether there exists a homology 3-sphere with certain knot properties.

method Constructing knots in contractible 4-manifolds and using Heegaard Floer homology invariants.

result Proves the existence of a class of deeply slice knots.

knot theory slice knots Heegaard Floer homology immersed curves 4-manifolds

2026-06-29abs ↗pdf ↗

Fixed-parameter tractable computation of Reshetikhin--Turaev knot polynomials via tensor networksmath.GT

New algorithm speeds up knot polynomial calculations.

problem Computing Reshetikhin--Turaev knot polynomials efficiently.

method Fixed-parameter tractable computation via tensor networks.

result Knot polynomial computations are fixed-parameter tractable.

knot theory Reshetikhin--Turaev tensor networks fixed-parameter tractable knot polynomials

2026-06-29abs ↗pdf ↗