Residue Formulas for the Large k Asymptotics of Witten's Invariants of Seifert Manifolds. The Case of SU(2)

TL;DR

This paper derives the large k asymptotics of SU(2) Witten's invariants for Seifert manifolds, expressing contributions of flat connections via residue formulas and intersection numbers.

Contribution

It introduces residue formulas for the asymptotics of Witten's invariants, linking contributions of irreducible connections to intersection theory.

Findings

Residue formulas for large k asymptotics derived

Contributions of irreducible connections expressed via intersection numbers

Moduli space components identified and analyzed

Abstract

We derive the large k asymptotics of the surgery formula for SU(2) Witten's invariants of general Seifert manifolds. The contributions of connected components of the moduli space of flat connections are identified. The contributions of irreducible connections are presented in a residue form. This form is similar to the one used by A. Szenes, L. Jeffrey and F. Kirwan. This similarity allows us to express the contributions of irreducible connections in terms of intersection numbers on their moduli spaces.