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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.

169,341 papers · 148 categories

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0111 · Mar 201219922001200920182026
5 results for “Birman-Series”
A Birman-Series type result for geodesics with infinitely many self-intersectionsmath.GT

Extended Birman-Series result to geodesics with infinitely many self-intersections.

problem Classifying geodesics with infinitely many self-intersections on hyperbolic surfaces.
method Defined a self-intersection function and extended the Birman-Series result to sets with bounded self-intersection functions.
result Same conclusion as Birman-Series for geodesics with self-intersection functions in o(l2)o(l^2).
geodesicsself-intersectionshyperbolic surfacesBirman-SeriesHausdorff dimension
2016-09-02abs ↗pdf ↗
A McShane-type identity for closed surfacesmath.DG

We prove a McShane-type identity - a series, expressed in terms of geodesic lengths, that sums to 2πfor any closed hyperbolic surface with one distinguished point. To do so, we prove a generalized Birman-Series theorem showing that the set of complete geodesics on a hyperbolic surface with large cone angles is sparse.

2012-03-17abs ↗pdf ↗
A Classification of Fundamental Group Elements Representing simple closed curves on the punctured Klein Bottlemath.GT

Classifies curves on a punctured Klein bottle, providing a counterexample to a loop conjecture.

problem Classifying curves on a punctured Klein bottle and addressing the simple loop conjecture.
method Explicit description of the mapping class group and classification of fundamental group elements.
result Provides a counterexample to the simple loop conjecture for Klein bottle representations.
Klein bottlefundamental groupcurvesmapping class groupsimple loop conjecture
2017-04-09abs ↗pdf ↗
McShane identities for Higher Teichmüller theory and the Goncharov-Shen potentialmath.GT

The paper extends McShane identities to higher Teichmüller theory and convex real projective surfaces.

problem Deriving McShane identities for higher Teichmüller theory.
method By studying mapping class group invariant functions and generalizing horocycle lengths.
result Established McShane-type identities for various surface group representations.
McShane identitieshigher Teichmüller theoryconvex real projective surfacesmapping class groupsurface group representations
2019-01-07abs ↗pdf ↗