Concordance group and stable commutator length in braid groups

Michael Brandenbursky, Jarek Kedra

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

We define a quasihomomorphism from braid groups to the concordance group of knots and examine its properties and consequences of its existence. In particular, we provide a relation between the stable four ball genus in the concordance group and the stable commutator length in braid groups, and produce examples of infinite families of concordance classes of knots with uniformly bounded four ball genus. We also provide applications to the geometry of the infinite braid group. In particular, we show that its commutator subgroup admits a stably unbounded conjugation invariant norm. This answers an open problem posed by Burago, Ivanov and Polterovich.
Original languageEnglish
Pages (from-to)2859-2884
Number of pages26
JournalAlgebraic & Geometric Topology
Volume15
Issue number5
DOIs
Publication statusPublished - 10 Dec 2015

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Keywords

  • braid group
  • concordance group
  • quasimorphism
  • conjugation invariant norm
  • commutator length
  • four ball genus

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