A NON-COMMUTATIVE REIDEMEISTER-TURAEV TORSION OF HOMOLOGY CYLINDERS

被引：1

作者：

Nozaki, Y. U. T. A. ^{[1
,2
]}

Sato, M. ^{[3
]}

Suzuki, M. ^{[4
]}

机构：

[1] Hiroshima Univ, Grad Sch Adv Sci & Engn, SKCM2, 1-3-1 Kagamiyama, Hiroshima 7398526, Japan

[2] Yokohama Natl Univ, Fac Environm & Informat Sci, 79 7 Toki wadai,Hodogaya ku, Yokohama 2408501, Japan

[3] Tokyo Denki Univ, Dept Math, 5 Senjuasahi cho,Adachi ku, Tokyo 1208551, Japan

[4] Meiji Univ, Dept Frontier Media Sci, 4-21 1 Nakano,Nakano ku, Tokyo 1648525, Japan

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2023年 / 376卷 / 07期

关键词：

Homology cylinder; surgery map; clasper; LMO functor; Reidemeister torsion; Enomoto-Satoh trace; K-1-group; FINITE-TYPE INVARIANTS; MAPPING CLASS-GROUPS; ABELIAN QUOTIENTS; TREE-LEVEL; REPRESENTATION; 3-MANIFOLDS; EQUIVALENCE; COBORDISMS; EXPANSION; SERIES;

D O I：

10.1090/tran/8925

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 Q pi(1)Sigma(g,1,) and prove that its reduction to (Q pi(1)Sigma(g,1)) over cap/(I) over cap (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.

引用

页码：5045 / 5088

页数：44

共 52 条

[1] On the Melvin-Morton-Rozansky conjecture [J].