A non-commutative Reidemeister-Turaev torsion of homology cylinders

Yuta Nozaki; Masatoshi Sato; Masaaki Suzuki

doi:10.1090/tran/8925

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arXiv · 2206.13019

A non-commutative Reidemeister-Turaev torsion of homology cylinders

Yuta Nozaki·Masatoshi Sato·Masaaki Suzuki

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Abstract

We compute the Reidemeister-Turaev torsion of homology cylinders which takes values in the $K_1$-group of the $I$-adic completion of the group ring $\mathbb{Q}\pi_1\Sigma_{g,1}$, and prove that its reduction to $\widehat{\mathbb{Q}\pi_1\Sigma_{g,1}}/\hat{I}^{d+1}$ is a finite-type invariant of degree $d$. We also show that the $1$-loop part of the LMO homomorphism and the Enomoto-Satoh trace can be recovered from the leading term of our torsion.

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Yuta Nozaki, Masatoshi Sato, Masaaki Suzuki. 2022-06-27. A non-commutative Reidemeister-Turaev torsion of homology cylinders. https://doi.org/10.1090/tran%2F8925

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