$\mathfrak{gl}(1 \vert 1)$-Alexander polynomial for $3$-manifolds

Autor:	Bao, Yuanyuan, Ito, Noboru
Rok vydání:	2022
Předmět:	Mathematics - Geometric Topology Primary 57K10 57K16 57K31
Druh dokumentu:	Working Paper
Popis:	As an extension of Reshetikhin and Turaev's invariant, Costantino, Geer and Patureau-Mirand constructed $3$-manifold invariants in the setting of relative $G$-modular categories, which include both semisimple and non-semisimple ribbon tensor categories as examples. In this paper, we follow their method to construct a $3$-manifold invariant from Viro's $\mathfrak{gl}(1\vert 1)$-Alexander polynomial. We take lens spaces $L(7, 1)$ and $L(7, 2)$ as examples to show that this invariant can distinguish homotopy equivalent manifolds. Comment: 18 pages. Comments are welcome
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2202.00238 Zobrazit plný text záznamu View this record from Arxiv