$\hat Z$- invariant for $SO(3)$ and $OSp(1|2)$ Groups

Sachin Chauhan; Pichai Ramadevi

doi:10.1007/s00023-023-01332-y

paper

$Z^$ - invariant for $S O (3)$ and $O S p (1∣2)$ Groups

arXiv:2209.00095 · doi:10.1007/s00023-023-01332-y

Abstract

Three-manifold invariants $Z^$ ('' $Z$ -hat''), also known as homological blocks, are $q$ -series with integer coefficients. Explicit $q$ -series form for $Z^$ is known for $S U (2)$ group, supergroup $S U (2∣1)$ and ortho-symplectic supergroup $O S p (2∣2)$ . We focus on $Z^$ for $S O (3)$ group and orthosymplectic supergroup $O S p (1∣2)$ in this paper. Particularly, the change of variable relating $S U (2)$ link invariants to the $S O (3)$ & $O S p (1∣2)$ link invariants plays a crucial role in explicitly writing the $q$ -series.

18 pages, 2 figures; minor changes; matches the published version

Cited by in corpus (1)

Quantum Modular $Z^{G}$ -Invariants

Z^- invariant for SO(3) and OSp(1∣2) Groups

Abstract

Cited by in corpus (1)

$Z^$ - invariant for $S O (3)$ and $O S p (1∣2)$ Groups