Arpan Kabiraj

collaborators

4 papers

math.GT2026

Poisson bracket of trace functions of Atiyah-Bott-Goldman symplectic structure on the Fuchsian locus of the $S L_{2} (R)$ character variety

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…

math.GT2026

Simple lift of non-simple closed curves

Deblina Das, Arpan Kabiraj

Given a compact, oriented surface $S$ of finite genus and finitely many boundary components, we provide examples of finite covers $S ~$ of $S$ and non-simple closed curves $Î…

math.GT2026

Non-injectivity of the trace map for character varieties

Deblina Das, Arpan Kabiraj

Given a closed oriented surface $I^£$ 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…

math.GT2026

Lifting closed curves to finite covers of free groups

Deblina Das, Arpan Kabiraj

In this article, we show that given any integer $l \geq 2$ , every closed curve $I^^{3}$ on the bouquet of $n$ -circles $I^$ , admits a lift to a finite $l$ -sheeted normal covering of $I^$ …

Poisson bracket of trace functions of Atiyah-Bott-Goldman symplectic structure on the Fuchsian locus of the SL2​(R) character variety

Simple lift of non-simple closed curves

Non-injectivity of the trace map for character varieties

Lifting closed curves to finite covers of free groups

Poisson bracket of trace functions of Atiyah-Bott-Goldman symplectic structure on the Fuchsian locus of the $S L_{2} (R)$ character variety