3 citations · 6 across the 12 of their papers we have counts for
13 papers
Turaev cobracket, synthetic geometry and applications
Moira Chas, Arpan Kabiraj
A teardrop geodesic on a hyperbolic surface is a closed curve that is geodesic except at exactly one point, called its vertex. One imagines a closed curve with one point held down…
Poisson bracket of trace functions on the Fuchsian locus and Wolpert's formulas
Deblina Das, Arpan Kabiraj
We develop a systematic method for computing traces of products of Möbius transformations associated with oriented geodesics on a hyperbolic surface. The method is based on a norma…
Non-injectivity of the trace map for character varieties
Deblina Das, Arpan Kabiraj
Given a closed oriented surface of genus at least two, the Goldman trace map defines a function from the vector space generated by the free homotopy classes of oriented closed…
Lifting closed curves to finite covers of free groups
Deblina Das, Arpan Kabiraj
In this article, we show that given any integer , every closed curve on the bouquet of -circles , admits a lift to a finite -sheeted normal covering of . E…
Simple lift of non-simple closed curves
Deblina Das, Arpan Kabiraj
Given a compact, oriented surface of finite genus and finitely many boundary components, we provide examples of finite covers of and non-simple closed curves $γ…
Explicit Lie bracket of closed geodesics on a hyperbolic surface with applications
Moira Chas, Arpan Kabiraj
In this note we develop a tool box of non-Euclidean plane geometry methods that yield a constructive way to define in terms of closed geodesics the Goldman bracket on deformation c…
Center of Poisson and skein algebras associated to loops on surfaces
Arpan Kabiraj
We discuss and develop a systematic method to compute the Poisson center (Casimir) of various Poisson algebras associated to loops on orientable surfaces (possibly with boundary an…
The Lie bracket of undirected curves on a surface
Moira Chas, Arpan Kabiraj
A Lie bracket defined on the linear span of the free homotopy classes of undirected closed curves was discovered in stages passing through Thurston's earthquake deformations, Wolpe…
On the entropy norm on the group of diffeomorphisms of closed oriented surface
Michael Brandenbursky, Arpan Kabiraj
We prove that the entropy norm on the group of diffeomorphisms of a closed orientable surface of positive genus is unbounded.
Elementary equivalence in Artin groups of finite type
Arpan Kabiraj, T. V. H. Prathamesh, Rishi Vyas
Irreducible Artin groups of finite type can be parametrized via their associated Coxeter diagrams into six sporadic examples and four infinite families, each of which is further pa…
Equal angles of intersecting geodesics for every hyperbolic metric
Arpan Kabiraj
We study the geometric properties of the terms of the Goldman bracket between two free homotopy classes of oriented closed curves in a hyperbolic surface. We provide an obstruction…
Goldman bracket and length equivalent filling curves
Arpan Kabiraj
A pair of distinct free homotopy classes of closed curves in an orientable surface with negative Euler characteristic is said to be length equivalent if for any hyperbolic stru…
Center Of the Goldman algebra
Arpan Kabiraj
We show that the center of the Goldman algebra associated to a closed oriented hyperbolic surface is trivial. For a hyperbolic surface of finite type with nonempty boundary, the ce…