Three-Manifold Quantum Invariants and Mock Theta Functions

Understand

Mock modular forms have found applications in numerous branches of mathematical sciences since they were first introduced by Ramanujan nearly a century ago.

• In this proceeding we highlight a new area where mock modular forms start to play an important role, namely the study of three-manifold invariants.
• For a certain class of Seifert three-manifolds, we describe a conjecture on the mock modular properties of a recently proposed quantum invariant.
• As an illustration, we include concrete computations for a specific three-manifold, the Brieskorn sphere $\Sigma(2,3,7)$.