A non-commutative Reidemeister-Turaev torsion of homology cylinders

Autor:	Nozaki, Yuta, Sato, Masatoshi, Suzuki, Masaaki
Rok vydání:	2022
Předmět:	Mathematics - Geometric Topology Mathematics - Quantum Algebra 57K16 57Q10 19B28 (Primary) 57K31 57K20 17B01 (Secondary)
Zdroj:	Trans. Amer. Math. Soc., electronically published on April 19, 2023
Druh dokumentu:	Working Paper
DOI:	10.1090/tran/8925
Popis:	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. Comment: 48 pages, 7 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2206.13019 Zobrazit plný text záznamu View this record from Arxiv