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2 results

  • Characterization of Positive Links and the s-invariant for Links

  • Tetsuya Abe, Keiji Tagami
  • Journal:
    Canadian Journal of Mathematics / Volume 69 / Issue 6 / 01 December 2017
    Published online by Cambridge University Press:
    20 November 2018, pp. 1201-1218
    Print publication:
    01 December 2017
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  • We characterize positive links in terms of strong quasipositivity, homogeneity, and the value of Rasmussen and Beliakova-Wehrli's $s$-invariant. We also study almost positive links, and in particular, determine the $s$-invariants of almost positive links. This result suggests that all almost positive links might be strongly quasipositive. On the other hand, it implies that almost positive links are never homogeneous links.

  • THE GENUS OF PERIODIC LINKS WITH RATIONAL QUOTIENTS

  • Part of
  • SANG YOUL LEE, MYOUNGSOO SEO
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 79 / Issue 2 / April 2009
    Published online by Cambridge University Press:
    13 March 2009, pp. 273-284
    Print publication:
    April 2009
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  • In this paper, we prove that if K is any periodic link in S3 whose quotient link is a 2-bridge link, then one half of the degree of the reduced Alexander polynomial, the minimal genus, the free genus and the canonical genus of K are all the same. We also give criteria to determine whether a given periodic link has a 2-bridge link quotient and some properties of this kind of periodic link.