Homological blocks with simple Lie algebras and Witten--Reshetikhin--Turaev invariants

TL;DR

This paper introduces homological blocks associated with simple Lie algebras for Seifert fibered homology 3-spheres and proves their radial limits correspond to Witten--Reshetikhin--Turaev invariants, using asymptotic analysis.

Contribution

It establishes a new connection between homological blocks and Witten--Reshetikhin--Turaev invariants for a class of 3-manifolds, with novel asymptotic formulas and vanishing results.

Findings

Homological blocks are defined for Seifert fibered homology 3-spheres.

Radial limits of these blocks match Witten--Reshetikhin--Turaev invariants.

Developed asymptotic formulas and proved vanishing of certain coefficients.

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.