Signatures in TQFT : Asymptotics and Modularity

Julien Marché, Gregor Masbaum

We study the signature ${\sigma }_g(\frac{q}{p})$ of ${\mathrm{SU}}_2$-TQFT vector spaces associated to surfaces of genus $g$, as a function of the defining root of unity $\zeta =e^{i\pi q/p}$. We pro…