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Homological blocks with simple Lie algebras and Witten--Reshetikhin--Turaev invariants
Yuya Murakami, Yuji Terashima
In this article, for any Seifert fibered homology 3-sphere, we introduce homological blocks with simple Lie algebra and prove that its radial limits are identified with the Witten-…
Quantum invariants of closed framed -manifolds based on ideal triangulations
Serban Matei Mihalache, Sakie Suzuki, Yuji Terashima
We construct a new type of quantum invariant of closed framed -manifolds with the vanishing first Betti number. The invariant is defined for any finite dimensional Hopf algebra,…
Witten-Reshetikhin-Turaev function for a knot in Seifert manifolds
Hiroyuki Fuji, Kohei Iwaki, Hitoshi Murakami +1
In this paper, for a Seifert loop (i.e., a knot in a Seifert three-manifold), first we give a family of an explicit function whose special values at roots of unity are id…
Cluster variables, ancestral triangles and Alexander polynomials
Wataru Nagai, Yuji Terashima
In this paper, we show that Alexander polynomials for any 2-bridge knots are specializations of cluster variables. A key tool is an ancestral triangle which appeared in both quantu…