$\mathfrak{gl}(1 \vert 1)$-Alexander polynomial for $3$-manifolds, Reidemeister torsion and lens spaces

Yuanyuan Bao

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arXiv · 2411.09923

$\mathfrak{gl}(1 \vert 1)$-Alexander polynomial for $3$-manifolds, Reidemeister torsion and lens spaces

Yuanyuan Bao

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Abstract

In this note, we reformulate the invariant $\Delta (M, \omega)$ that we defined before, and show its relation with Reidemeister torsion. We calculate $\Delta (M, \omega)$ when the $3$-manifolds are lens spaces, and discuss the classification of the lens spaces using $\Delta (M, \omega)$.

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Yuanyuan Bao. 2024-11-15. $\mathfrak{gl}(1 \vert 1)$-Alexander polynomial for $3$-manifolds, Reidemeister torsion and lens spaces. https://arxiv.org/abs/2411.09923

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