\mathfrakgl(1 \vert 1)-Alexander polynomial for 3-manifolds

2022/02/01 by Yuanyuan Bao, Noboru Ιτο, Bao, Yuanyuan +1
Mathematics · #57K16 #57K31 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology #Primary 57K10

paper · pdf · doi:10.48550/arxiv.2202.00238

openalex publication_date 2022/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 \mathfrakgl(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.

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