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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.

168,695 papers · 148 categories

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7 results for “non-characterizing”

Knots with infinitely many non-characterizing slopesmath.GT

Study confirms infinitely many non-characterizing slopes for various knots.

problem Determining knots with infinitely many non-characterizing slopes.

method Techniques on annulus twists to observe and prove infinitely many non-characterizing slopes.

result Proves infinitely many non-characterizing slopes for multiple knots.

knots infinitely many non-characterizing slopes annulus twists 6_3 6_2

2020-03-16abs ↗pdf ↗

Certain connect sums of torus knots with infinitely many non-characterizing slopesmath.GT

Certain torus knots have infinitely many slopes that do not uniquely identify them.

problem Identifying non-characterizing slopes for certain torus knots.

method Applying a condition from Baker and Motegi to show infinitely many non-characterizing slopes.

result The knots

T_{2,2n+3}\#T_{-2,2n+1}

have infinitely many non-characterizing slopes.

torus knots non-characterizing slopes surgery Baker-Motegi condition

2023-02-10abs ↗pdf ↗

Knots not detected by any tracemath.GT

New knots found that resist trace detection.

problem Knots not detected by any trace.

method Extended existing results to new knots.

result Knots exist that share traces with infinitely many distinct knots and are not detected by any trace.

knot theory trace concordance integer slope non-characterizing

2025-03-18abs ↗pdf ↗

Non-characterizing slopes for hyperbolic knotsmath.GT

A non-trivial slope $r$ on a knot $K$ in $S^3$ is called a characterizing slope if whenever the result of $r$ -surgery on a knot $K'$ is orientation preservingly homeomorphic to the result of $r$ -surgery on $K$ , then $K'$ is isotopic to $K$ . Ni and Zhang ask: for any hyperbolic knot $K$ , is a slope $r = p/q$ with $|p| +…