A note on quantum 3-manifold invariants and hyperbolic volume
Efstratia Kalfagianni
TL;DR
This paper explores the conjectured link between quantum invariants and hyperbolic volume, providing examples of manifolds with identical invariants but different volumes, challenging existing conjectures.
Contribution
It constructs hyperbolic 3-manifolds with matching quantum invariants at specified levels but differing volumes, offering new insights into the invariants-volume relationship.
Findings
Existence of manifolds with identical invariants at given levels
Counterexamples to conjectured invariants-volume correlation
Implications for quantum topology theories
Abstract
We investigate the conjectural relations between the Reshetikhin-Turaev-Witten quantum SU(2) invariants and the volume of hyperbolic 3-manifolds. Given a finite set of sufficiently large positive integers, say J, we construct examples of closed hyperbolic 3-manifolds with the same invariants at all levels in J and different volume.
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Combinatorial Mathematics · Advanced Operator Algebra Research