An addendum on iterated torus knots
Abstrak
In Theorem 1.2 of the paper math.GT/0002110 the author claimed to have proved that all transversal knots whose topological knot type is that of an iterated torus knot (we call them cable knots) are transversally simple. That theorem is false, and the Erratum math.GT/0610565 identifies the gap. The purpose of this paper is to explore the situation more deeply, in order to pinpoint exactly which cable knots are {\it not} transversally simple. The class is subtle and interesting. We will recover the strength of the main theorem in math.GT/0002110, in the sense that we will be able to prove a strong theorem about cable knots, but the theorem itself is more subtle than Theorem 1.2 of math.GT/0002110. In particular, we give a geometric realization of the Honda-Etnyre transverse (2,3)-cable of the (2,3)-torus knot example (Appendix joint with H. Matsuda). (See math.SG/0306330)
Topik & Kata Kunci
Penulis (1)
W. Menasco
Akses Cepat
PDF tidak tersedia langsung
Cek di sumber asli →- Tahun Terbit
- 2006
- Bahasa
- en
- Total Sitasi
- 9×
- Sumber Database
- Semantic Scholar
- Akses
- Open Access ✓