Z-hat three-manifold invariants are shown to depend only on the Lie algebra, and a quiver matrix block structure is conjectured for double twist knots.
Homological blocks with simple Lie algebras and Witten--Reshetikhin--Turaev invariants
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abstract
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--Reshetikhin--Turaev invariants. To prove it, we develop an asymptotic formula and a vanishing result of asymptotic coefficients.
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$q$-Series Invariants of Three-Manifolds and Knots-Quivers Correspondence
Z-hat three-manifold invariants are shown to depend only on the Lie algebra, and a quiver matrix block structure is conjectured for double twist knots.