arXiv Open Access 2000

Vassiliev invariants of Legendrian, of transverse and framed knots in contact 3-manifolds

Vladimir Tchernov

Lihat Sumber

Abstrak

We show that for a large class of contact 3-manifolds the groups of Vassiliev invariants of Legendrian and of framed knots are canonically isomorphic. As a corollary, we obtain that the group of finite order Arnold's $J^+$-type invariants of wave fronts on a surface $F$ is isomorphic to the group of Vassiliev invariants of framed knots in the spherical cotangent bundle $ST^*F$ of $F$. On the other hand we construct the first examples of contact manifolds for which Vassiliev invariants of Legendrian knots can distinguish Legendrian knots that realize isotopic framed knots and are homotopic as Legendrian immersions.

Topik & Kata Kunci

math.SG math.GT

Penulis (1)

Vladimir Tchernov

Format Sitasi

APA MLA BibTeX

Tchernov, V. (2000). Vassiliev invariants of Legendrian, of transverse and framed knots in contact 3-manifolds. https://arxiv.org/abs/math/0005002

Akses Cepat

Lihat di Sumber

Informasi Jurnal

Tahun Terbit: 2000
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓