Work

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

Year: 2022

Type: preprint

Abstract: 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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2202.00238

Authors: Bao, Yuanyuan, Ito, Noboru

Institutions: Ibaraki National College of Technology, The University of Tokyo

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Toyohashi University of Technology, Japan Society for the Promotion of Science

Award: Study of categorificaitons of Vassiliev invariants

OpenAlex ID: W4226099986

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