论文标题
Turaev-Viro TQFT和等级与属的猜想
Turaev-Viro TQFT and the Rank versus Genus Conjecture
论文作者
论文摘要
本文提出了一种使用Turaev-Viro State Sum TQFT估算$ 3 $ manifold的Heegaard属的方法。 turaev-viro state sum tqft衍生自与量子组$ u_q（\ mathfrak {sl} _2）$相关的模块化类别，这是Wenzl的一些$ q $的单位。因此，Turaev和Virelizier相应的TQFT是统一的。我们通过Garoufalidis修改了使用单一TQFT的Heegaard Genus的下限，然后使用软件Regina为Regina提供了一些已知的反示例，以与属属构想相比。
This paper presents a way to estimate the Heegaard genus of a $3$-manifold using the Turaev-Viro state sum TQFT. The Turaev-Viro state sum TQFT is derived from the modular category associated to the quantum group $U_q(\mathfrak{sl}_2)$, which is unitary for some $q$ by Wenzl. Hence by Turaev and Virelizier the corresponding TQFT is unitary. We modify a proof by Garoufalidis to give a lower bound of the Heegaard genus using a unitary TQFT, and then use the software Regina to provide some known counterexamples to the rank versus genus conjecture.
