Bibliographie générale

Costantino, Charlotte; Fejtö, Kalyane; Havas, Roland

doi:10.3917/puf.costa.2018.01.0233

Cited by 1 publication

(1 citation statement)

References 16 publications

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“…Even in the case of closed 3−manifolds, for example S 2 × S 1 #S 2 × S 1 , the kernel of the Chebyshev homomorphism may have non-trivial kernel. This will be explored in upcoming work of the second author and Constantino [CL2]. 4.10.…”

Section: φωmentioning

confidence: 99%

The Chebyshev-Frobenius homomorphism for stated skein modules of 3-manifolds

Bloomquist¹,

Le²

2020

Preprint

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We study the stated skein modules of marked 3−manifolds. We generalize the splitting homomorphism for stated skein algebras of surfaces to a splitting homomorphism for stated skein modules of 3−manifolds. We show that there exists a Chebyshev-Frobenius homomorphism for the stated skein modules of 3-manifolds which extends the Chebyshev homomorphism of the skein algebras of unmarked surfaces originally constructed by Bonahon and Wong. Additionally, we show that the Chebyshev-Frobenius map commutes with the splitting homomorphism. This is then used to show that in the case of the stated skein algebra of a surface, the Chebyshev-Frobenius map is the unique extension of the dual Frobenius map (in the sense of Lusztig) of O q 2 (SL(2)) through the triangular decomposition afforded by an ideal triangulation of the surface. In particular, this gives a skein theoretic construction of the Hopf dual of Lusztig's Frobenius homomorphism. A second conceptual framework is given, which shows that the Chebyshev-Frobenius homomorphism for the stated skein algebra of a surface is the unique restriction of the Frobenius homomorphism of quantum tori through the quantum trace map.

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Section: φωmentioning

confidence: 99%