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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.

169,051 papers · 148 categories

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6 results for “arccosh”

Systoles of hyperbolic surfaces with big cyclic symmetrymath.GT

Exact systole values found for hyperbolic surfaces with specific cyclic symmetries.

problem Finding exact systole lengths for hyperbolic surfaces with maximal cyclic symmetries.

method Analyzing hyperbolic surfaces of different genera with specified cyclic symmetries and calculating exact systole lengths.

result Exact formulas for systole lengths of hyperbolic surfaces with maximal cyclic symmetries.

systoles hyperbolic surfaces cyclic symmetry genus arccosh

2018-12-13abs ↗pdf ↗

The shortest non-simple closed geodesics on hyperbolic surfacesmath.GT

Shortest non-simple closed geodesics on hyperbolic surfaces found.

problem Finding the shortest non-simple closed geodesics on hyperbolic surfaces.

method Analyzing closed geodesics with at least k self-intersections on hyperbolic surfaces.

result The shortest non-simple closed geodesics lie on an ideal pair of pants and have length $2\arccosh(2k+1)$.

hyperbolic surfaces closed geodesics non-simple ideal pair of pants self-intersections

2022-10-24abs ↗pdf ↗

The asymptotic behaviors of the colored Jones polynomials of the figure eight-knot, and an affine representationmath.GT

Study shows exponential growth of knot polynomial tied to Chern-Simons invariant.

problem Asymptotic behavior of colored Jones polynomials of figure-eight knot.

method Analyzes growth rate of polynomial evaluated at specific points.

result Growth rate determined by Chern-Simons invariant of an affine representation.

Jones polynomial figure-eight knot Chern-Simons invariant affine representation exponential growth

2023-07-14abs ↗pdf ↗

The colored Jones polynomial of the figure-eight knot and an

\operatorname{SL}(2;\mathbb{R})

-representationmath.GT

The colored Jones polynomial of the figure-eight knot connects to an SL(2;R) representation.

problem Asymptotic behavior of colored Jones polynomial for the figure-eight knot.

method Analyzing the polynomial's behavior as N approaches infinity and evaluating it at specific points.

result The polynomial corresponds to an SL(2;R) representation of the knot complement.

colored Jones polynomial figure-eight knot SL(2;R) representation fundamental group Reidemeister torsion

2023-12-01abs ↗pdf ↗

Maximal systole of hyperbolic surface with largest

S^3

extendable abelian symmetrymath.GT

Formula found for maximal systole of hyperbolic surfaces with largest $S^3$ symmetry.

problem Finding the maximal systole of hyperbolic surfaces with largest

S^3

extendable abelian symmetry.

method Derived a formula involving

L

and

K

to calculate the maximal systole.

result The maximal systole is given by

2\mathrm{arccosh} K

systole hyperbolic surface S^3 symmetry maximal abelian group

2019-11-24abs ↗pdf ↗

An infinite product on the Teichmüller space of the once-punctured torusmath.GT

The paper proves an infinite product identity on the Teichmüller space of a once-punctured torus.

problem An infinite product identity on the Teichmüller space of a once-punctured torus.

method Elementary proof by integrating around a chosen triple of geodesics in its Teichmüller orbit.

result Proves an identity involving lengths and traces of geodesics on the once-punctured torus.

Teichmüller space once-punctured torus infinite product geodesics height

2020-01-15abs ↗pdf ↗