Brunnian links, claspers and Goussarov-Vassiliev finite type invariants

• Autores: Kazuo Habiro
• Localización: Mathematical proceedings of the Cambridge Philosophical Society, ISSN 0305-0041, Vol. 142, Nº 3, 2007, págs. 459-468
• Idioma: inglés
• DOI: 10.1017/s0305004107000072
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• Resumen

  • Goussarov and the author independently proved that two knots in S3 have the same values of finite type invariants of degree

    In this paper, we study the case of Brunnian links, which are links whose proper sublinks are trivial. We prove that if n = 1, then an (n+1)-component Brunnian link L is Cn-equivalent to an unlink. We also prove that if n = 2, then L can not be distinguished from an unlink by any Goussarov¿Vassiliev finite type invariant of degree <2n.