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pro vyhledávání: '"Santharoubane, Ramanujan"'
In this paper, we study the kernels of the $\mathrm{SO}(3)$-Witten-Reshetikhin-Turaev quantum representations $\rho_p$ of mapping class groups of closed orientable surfaces $\Sigma_g$ of genus $g.$ We investigate the question whether the kernel of $\
Externí odkaz:
http://arxiv.org/abs/2309.11906
For any irreducible representation of a surface group into $\mathrm{SL}_2(\mathbb{C})$, we show that there exists a pants decomposition where the restriction to any pair of pants is irreducible and where no curve of the decomposition is sent to a tra
Externí odkaz:
http://arxiv.org/abs/2210.09854
We construct embeddings of Kauffman bracket skein algebras of surfaces (either closed or with boundary) into localized quantum tori using the action of the skein algebra on the skein module of the handlebody. We use those embeddings to study represen
Externí odkaz:
http://arxiv.org/abs/2205.03291
Autor:
Santharoubane, Ramanujan
Publikováno v:
Algebr. Geom. Topol. 24 (2024) 2571-2578
Let $\Sigma$ be a surface with negative Euler characteristic, genus at least one and at most one boundary component. We prove that the skein algebra of $\Sigma$ over the field of rational functions can be algebraically generated by a finite number of
Externí odkaz:
http://arxiv.org/abs/1803.09804
Let $(S,\, \ast)$ be a closed oriented surface with a marked point, let $G$ be a fixed group, and let $\rho\colon\pi_1(S) \longrightarrow G$ be a representation such that the orbit of $\rho$ under the action of the mapping class group $Mod(S,\, \ast)
Externí odkaz:
http://arxiv.org/abs/1702.03622
We prove that the Witten--Reshetikhin--Turaev $\mathrm{SU}(2)$ quantum representations of mapping class groups are always irreducible in the case of surfaces equipped with colored banded points, provided that at least one banded point is colored by o
Externí odkaz:
http://arxiv.org/abs/1701.08901
For a banded link $L$ in a surface times a circle, the Witten-Reshetikhin-Turaev invariants are topological invariants depending on a sequence of complex $2p$-th roots of unity $(A_p)_{p\in 2\mathbb{N}}$. We show that there exists a polynomial $P_L$
Externí odkaz:
http://arxiv.org/abs/1607.00664
Autor:
Santharoubane, Ramanujan
For $n$ an even number, we study representations of the mapping class group of the $n$-punctured sphere arising from $\mathrm{SU}(2)$-TQFT when all punctures are colored by the same integer $N \geq 1$. We prove that the conjecture of Andersen, Masbau
Externí odkaz:
http://arxiv.org/abs/1606.02568
We produce a sequence of finite dimensional representations of the fundamental group $\pi_1(S)$ of a closed surface where all simple closed curves act with finite order, but where each non--simple closed curve eventually acts with infinite order. As
Externí odkaz:
http://arxiv.org/abs/1603.03456
We prove that for each sufficiently complicated orientable surface $S$, there exists an infinite image linear representation $\rho$ of $\pi_1(S)$ such that if $\gamma\in\pi_1(S)$ is freely homotopic to a simple closed curve on $S$, then $\rho(\gamma)
Externí odkaz:
http://arxiv.org/abs/1510.00677