Reidemeister–Turaev torsion of 3-dimensional¶Euler structures with simple boundary tangency¶and pseudo-Legendrian knots
Reidemeister–Turaev torsion of 3-dimensional¶Euler structures with simple boundary tangency¶and pseudo-Legendrian knots
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3 维的 Reidemeister-Turaev 扭转“具有简单边界相切的欧拉结构”和伪勒让德结
DOI：
10.1007/s002290100191
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发表时间：
2000
影响因子：
0.6
通讯作者：
C. Petronio
中科院分区：
文献类型：
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作者：
R. Benedetti;C. Petronio
摘要：我们推广了 Turaev 对 (M,&\xi;) 扭转不变量的定义，其中 M 是一个 3 维流形，&\xi;是 M 上的欧拉结构（相对于 ∂M 达到同伦的非奇异向量场以及 Int(M) 中包含的球中支持的修改）。也就是说，我们允许 M 有任意边界并且 &\xi;与边界有简单的（凸和/或凹）相切圆。我们证明 Turaev 的 H1(M) 等方差公式在我们的广义背景下也成立。使用分支标准脊柱对矢量场进行编码，我们展示了如何将图拉耶夫的重建图从组合显式反转为平滑欧拉结构，从而使扭转的计算更加有效。我们认为这种欧拉结构自然出现在伪勒让德结（即横向于给定向量场的结）以及接触 3 流形中的勒让德结的研究中。我们证明，挠率作为绝对不变量，包含对经典亚历山大不变量的伪勒让德结的提升。我们还精确分析了扭转所携带的信息作为框架同位素伪勒让德结的相对不变量。
Abstract: We generalize Turaev's definition of torsion invariants of pairs (M,&\xi;), where M is a 3-dimensional manifold and &\xi; is an Euler structure on M (a non-singular vector field up to homotopy relative to ∂M and modifications supported in a ball contained in Int(M)). Namely, we allow M to have arbitrary boundary and &\xi; to have simple (convex and/or concave) tangency circles to the boundary. We prove that Turaev's H1(M)-equivariance formula holds also in our generalized context. Using branched standard spines to encode vector fields we show how to explicitly invert Turaev's reconstruction map from combinatorial to smooth Euler structures, thus making the computation of torsions a more effective one. Euler structures of the sort we consider naturally arise in the study of pseudo-Legendrian knots (i.e.~knots transversal to a given vector field), and hence of Legendrian knots in contact 3-manifolds. We show that torsion, as an absolute invariant, contains a lifting to pseudo-Legendrian knots of the classical Alexander invariant. We also precisely analyze the information carried by torsion as a relative invariant of pseudo-Legendrian knots which are framed-isotopic.
3-流形相对微分同胚群分类空间的有限性
DOI：
--
发表时间：
1997
期刊：
影响因子：
--
作者：
A. Hatcher;Darryl McCullough
通讯作者：
Darryl McCullough