Quantum Approach to Dehn Surgery Problem

Dongmin Gang

Quantum Approach to Dehn Surgery Problem

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arxiv 1803.11143 v2 pith:KCUZYYFU submitted 2018-03-29 math.GT hep-thquant-ph

Quantum Approach to Dehn Surgery Problem

Dongmin Gang This is my paper

classification math.GT hep-thquant-ph

keywords dehnalgorithminvariantmanifoldproblemquantumsurgeryapproach

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We propose a new algorithm for Dehn surgery problem, finding exceptional Dehn filling slopes for a given hyperbolic 3-manifold with a torus boundary, using a quantum invariant called "3D index". The invariant is defined using an ideal triangulation of the cusped 3-manifold. We test the algorithm for many examples.

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Refined 3D index
hep-th 2026-04 unverdicted novelty 7.0

A refined 3D index is defined by adding flavor symmetry gradings to the superconformal index of T[M], yielding an explicit infinite-sum formula from Dehn surgery that is claimed to be a strictly stronger invariant tha...