𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Incompressible surfaces in tunnel number one knot complements

✍ Scribed by Mario Eudave-Muñoz

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
305 KB
Volume
98
Category
Article
ISSN
0166-8641

No coin nor oath required. For personal study only.

✦ Synopsis

A knot k in S 3 has tunnel number one, if there exist an arc τ embedded in S 3 , with k ∩ τ = ∂τ , such that S 3int N(k ∪ τ ) is a genus 2 handlebody.

In this paper we construct for each integer g 2, infinitely many tunnel number one knots, whose complement contain a closed incompressible surface of genus g.

📜 SIMILAR VOLUMES

Incompressible pairwise incompressible s
Incompressible pairwise incompressible surfaces in almost alternating knot complements
✍ Han You Fa 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 706 KB

In this paper, we deal with incompressible pairwise incompressible surfaces in almost alternating knot complements. We show that the genus of a surface in an almost alternating knot exterior equals zero if there are two, four or six boundary components in the surface.

Tubed incompressible surfaces in knot an
Tubed incompressible surfaces in knot and link complements
✍ Elizabeth Finkelstein; Yoav Moriah 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 260 KB

We prove that the complements of all knots and links in S 3 which have a 2n-plat projection with absolute value of all twist coefficients bigger than 2 contain closed embedded incompressible nonboundary parallel surfaces. These surfaces are obtained from essential planar meridional surfaces by tubin

Closed incompressible surfaces in comple
Closed incompressible surfaces in complements of wide knots and links
✍ Martin Lustig; Yoav Moriah 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 806 KB

We define the notion of wide knots (and links) and show that they contain closed incompressible nonboundary parallel surfaces in their complement. This is done by proving that these complements admit Heegaard splittings which are irreducible but weakly reducible, and using an extension of a result o