论文标题
同源缸的非交流性雷德氏菌扭转
A non-commutative Reidemeister-Turaev torsion of homology cylinders
论文作者
论文摘要
我们计算同源气缸的reidemeister-turaev扭转，该圆柱体在$ k_1 $ - 群体中的$ i $ - adic完成$ i $ - adic的完成$ \ mathbb {q}π_1σ_{g，1} $ $ \ wideHat {\ mathbb {q}π_1σ_{g，1}}}/\ hat {i}^{d+1} $是$ d $的有限型不变性。我们还表明，可以从我们的扭转的领先术语中回收LMO同构和Inomoto-satoh跟踪的$ 1 $ - 环部分。
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 $\mathbb{Q}π_1Σ_{g,1}$, and prove that its reduction to $\widehat{\mathbb{Q}π_1Σ_{g,1}}/\hat{I}^{d+1}$ 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.
