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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·8 papers on “3-manifolds” in Geometric Topology · 1 month

Genus-zero links with prescribed knots as componentsmath.GT

Proves any three or more knots can form a genus-zero link in a 3-manifold.

problem Realizing any finite collection of knots as components of a genus-zero link.

method Proves the realizability of knots as components of genus-zero links in 3-manifolds, controlling pairwise linking numbers.

result Any finite collection of at least three isotopy classes of knots can form a genus-zero link in a 3-manifold, satisfying a specific condition.

genus-zero links knots 3-manifolds pairwise linking numbers isotopy classes

2026-07-14abs ↗pdf ↗

Finiteness of pseudo-Anosov flows without perfect fitsmath.GT

Finitely many pseudo-Anosov flows without perfect fits in a 3-manifold.

problem Finite number of pseudo-Anosov flows without perfect fits in a 3-manifold.

method Analysis of veering triangulations and pseudo-Anosov flows.

result Finiteness of pseudo-Anosov flows without perfect fits.

pseudo-Anosov flows 3-manifolds veering triangulations finiteness

2026-07-11abs ↗pdf ↗

Homological Topological Quantum Field Theoriesmath.GT

New framework for quantum invariants of 3-manifolds using homology.

problem Quantum invariants of 3-manifolds.

method Homological construction of mapping class group representations extended to cobordisms.

result Construction of a

(2+1)

-dimensional TQFT assigning twisted homology to surfaces.

quantum invariants 3-manifolds topological quantum field theory homology mapping class group

2026-07-10abs ↗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 ↗

Simultaneous universal circles and continuous extensionmath.GT

An alternate proof shows how foliation extensions work in 3D spaces.

problem Continuous extension of foliations in 3D spaces.

method Uses the universal circle and properties of pseudo-Anosov flows.

result Shows how all continuous extensions organize in the boundary.

foliations 3-manifolds pseudo-Anosov universal circle continuous extension

2026-07-06abs ↗pdf ↗

On the fiberedness of surgery 3-manifoldsmath.GT

Dehn surgery on knots in 3-manifolds rarely results in surface fibered manifolds.

problem Understanding when Dehn surgery on knots in 3-manifolds results in surface fibered manifolds.

method Analyzing the fiberedness of Dehn surgeries on knots in 3-manifolds.

result Dehn surgery on knots in 3-manifolds is not surface fibered for all but a sparse set of slopes.

Dehn surgery 3-manifolds fibered manifolds sparse set knots

2026-06-28abs ↗pdf ↗

Multi-framed real monopole Floer theorymath.GT

The paper develops a new Floer theory for 3-manifolds with involutions.

problem Constructing a Floer theory for 3-manifolds with symmetries.

method Develops a framed real monopole Floer homology for 3-manifolds with involutions and provides definitions for invariants.

result Defines

\mathbf{Z}

-valued framed real Seiberg--Witten invariants for 4-manifolds with involutions.

Floer homology 3-manifolds involutions invariants Seiberg-Witten

2026-06-26abs ↗pdf ↗

A Combinatorial Characterization of Sol 3-Manifoldsmath.GT

A universal branched 3-manifold $W$ characterizes Sol 3-manifolds.

problem Characterizing Sol 3-manifolds

method Using a universal branched 3-manifold

W

and a regular language

result A closed 3-manifold

M

immerses into

W

if and only if

M

admits a Sol structure.

Sol 3-manifolds triangulation universal branched 3-manifold

2026-06-22abs ↗pdf ↗