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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.

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8 results for “Kirby-Thompson”

Some lower bounds for the Kirby-Thompson invariantmath.GT

The paper sets lower bounds for a Kirby-Thompson invariant of 4-manifolds.

problem Determining the Kirby-Thompson invariant of specific 4-manifolds.

method Using trisections, the paper establishes lower bounds and calculates the invariant for specific examples.

result The paper calculates the Kirby-Thompson invariant of the spin of

L(2,1)

and shows the existence of 4-manifolds with arbitrarily large invariants.

Kirby-Thompson invariant 4-manifolds trisections lower bounds non-trivial invariants

2023-02-15abs ↗pdf ↗

Bounding the Kirby-Thompson invariant of spun knotsmath.GT

New bounds found for complexity of spun knots.

problem Measuring complexity of spun knots.

method Using bridge trisections and distances in the pants complex.

result Bound the Kirby-Thompson invariant of spun knots.

spun knots Kirby-Thompson invariant bridge trisection pants complex

2021-12-04abs ↗pdf ↗

Bounds for Kirby-Thompson invariants of knotted surfacesmath.GT

Sharp bounds for Kirby-Thompson invariants of knotted surfaces computed.

problem Computing sharp lower bounds for Kirby-Thompson invariants of knotted surfaces.

method Using dual curve complex distances to compute invariants.

result Exact values of KT-invariants computed for knotted surfaces with bridge number ≤ 6.

Kirby-Thompson invariants knotted surfaces dual curve complex bridge number

2022-06-06abs ↗pdf ↗

Trisections with Kirby-Thompson length 2math.GT

This paper proves a conjecture about trisections with a specific length.

problem Proving a conjecture about trisections with a specific length.

method Examining trisections with Kirby-Thompson length 2 and proving the conjecture.

result Proves the conjecture about length 2 trisection being a 4-manifold with length 0.

trisection length 2 Kirby-Thompson 4-manifold conjecture

2021-12-19abs ↗pdf ↗

Kirby-Thompson distance for trisections of knotted surfacesmath.GT

New invariant measures knotted surfaces in 4D, revealing unknottedness.

problem Measuring knotted surfaces in 4D.

method Defined an integer invariant

\mathcal{L}(\mathcal{T})

for bridge trisections of surfaces in

S^4

B^4

result Invariant

\mathcal{L}(\mathcal{T})=0

implies the surface is unknotted.

trisection bridge number 4D Kirby-Thompson Zupan

2020-02-10abs ↗pdf ↗

Estimating the Kirby--Thompson Invariants of Surface-Links in the Yoshikawa Tablemath.GT

Upper bounds for surface-links in the Yoshikawa table are estimated.

problem Estimating Kirby-Thompson invariants of surface-links.

method Using tri-plane diagrams and L-, L*-invariants.

result Upper bounds for surface-links in the Yoshikawa table are obtained.

surface-links Yoshikawa table Kirby-Thompson invariants tri-plane diagrams L-invariants

2025-11-18abs ↗pdf ↗

The contact cut graph and a Weinstein

\mathcal{L}

-invariantmath.GT

New invariant defined for Weinstein domains, related to Kirby-Thompson's invariant.

problem Defining a symplectic invariant for Weinstein domains.

method Contact cut graph, Lefschetz fibrations, multisections with divides.

result Definition of Weinstein

\mathcal{L}

-invariant and its relation to Kirby-Thompson's invariant.

Weinstein domain Lefschetz fibration contact geometry symplectic invariant Kirby-Thompson invariant

2024-08-09abs ↗pdf ↗

Kirby-Thompson invariants of distant sums of standard surfacesmath.GT

Paper calculates L-invariant and L*-invariant for complex surface sums.

problem Calculating invariants for complex surface sums.

method Using pants complexes and dual curve complexes.

result First example of arbitrary large invariants for bridge numbers.

Kirby-Thompson invariants knotted surfaces distant sums standard surfaces L-invariant

2024-05-11abs ↗pdf ↗