On the quasitoric braid index of a link

Yongju Bae, Seogman Seo

Research output: Contribution to journalArticlepeer-review

Abstract

We dene new link invariants which are called the quasitoric braid index and the cyclic length of a link and show that the quasitoric braid index of link with k components is the product of k and the cy- cle length of link. Also, we give bounds of Gordian distance between the (p; q)-torus knot and the closure of a braid of two specic quasitoric braids which are called an alternating quasitoric braid and a blockwise alternat- ing quasitoric braid. We give a method of modication which makes a quasitoric presentation from its braid presentation for a knot with braid index 3. By using a quasitoric presentation of 10139 and 10124, we can prove that u(10139) = 4 and d ×(10124;K(3; 13)) = 8.

Original languageEnglish
Pages (from-to)1305-1321
Number of pages17
JournalJournal of the Korean Mathematical Society
Volume52
Issue number6
DOIs
StatePublished - 2015

Keywords

  • Braid
  • Braid index
  • Knot
  • Link
  • Qua-sitoric braid index
  • Quasitoric braid
  • Toric braid

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