Skeins on tori

S Gunningham, D Jordan, M Vazirani - arXiv preprint arXiv:2409.05613, 2024 - arxiv.org
… We analyze the G-skein theory invariants of the 3-torus T3 … skein module of T3, and we
describe the algebraic structure of the skein category of T2 – namely of the n-point relative skein

Skein module dimensions of mapping tori of the 2-torus

P Kinnear - arXiv preprint arXiv:2304.07332, 2023 - arxiv.org
… In §2, after recalling some background on mapping tori, we explain how to decompose SkG(…
the skein category, building on work of [GJVY]. We take care to set up the definitions of skein

An embedding of skein algebras of surfaces into quantum tori from Dehn-Thurston coordinates

R Detcherry, R Santharoubane - arXiv preprint arXiv:2205.03291, 2022 - arxiv.org
… M = Σ×[0,1], with Σ a compact oriented surface, the skein … We will write S(Σ) for the skein
algebra of a surface (ie the skein … , the skein module S(M) is a module over the skein algebra S(∂…

The skein valued mirror of the topological vertex

T Ekholm, P Longhi, V Shende - arXiv preprint arXiv:2412.15454, 2024 - arxiv.org
skein module of the union of the tori. Using 1-parameter families of curves at infinity, we
derive three skein … We will consider the action of the Ai on the skein of the triple of solid tori in …

Quantum traces and embeddings of stated skein algebras into quantum tori

TTQ Lê, T Yu - Selecta Mathematica, 2022 - Springer
skein algebra of a punctured bordered surface with non-empty boundary can be embedded
into quantum tori … version of the stated skein algebra. As applications we show that the stated …

[PDF][PDF] The skein module of torus knots complements

J Marché - ArXiv e-prints - Citeseer
… In the remaining part of T foliated by tori {|z| = λ} we interpolate between the map given by
Φs on λ = 1 − ε and the identity on λ = 1. This shows that τ2kγ is isotopic to γ and so that τ2k is …

[PDF][PDF] GEAR PROBLEMS IN SKEIN THEORY

C FROHMAN - math.fsu.edu
… mutative tori that are in analogy with theorems that have been proved about the skein
algebra. The fourth problem set are open problems in the theory of the Kauffman bracket skein

On torsion in the Kauffman bracket skein module of -manifolds

G Belletti, R Detcherry - arXiv preprint arXiv:2406.17454, 2024 - arxiv.org
… In this paper we provide effective criteria, based on representation theory, to find torsion in
skein modules arising from essential tori; in particular we are able to use them to prove the …

Reflection equation and link polynomials for arbitrary genus solid tori

C Schwiebert - arXiv preprint hep-th/9301023, 1993 - arxiv.org
… reflection equation matrix is considered as an additional skein relation. This could lead to
an intrinsic definition of invariant link polynomials on solid tori and, via Heegaard splitting, to …

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

W Bloomquist, TTQ Lê - Mathematische Zeitschrift, 2022 - Springer
… In particular, this gives a skein theoretic construction of the Hopf dual of Lusztig’s … skein
algebra of a surface is the unique restriction of the Frobenius homomorphism of quantum tori