3 papers
math.GT2024
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…
math.GR2019
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…
math.GT2018
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.