Concordance group and stable commutator length in braid groups

Michael Brandenbursky, Jarek Kędra

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

We define quasihomomorphisms from braid groups to the concordance group of knots and examine their properties and consequences of their 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 B. In particular, we show that the commutator subgroup [B,B] admits a stably unbounded conjugation invariant norm. This answers an open problem posed by Burago, Ivanov and Polterovich.

Original languageEnglish
Pages (from-to)2861-2886
Number of pages26
JournalAlgebraic and Geometric Topology
Volume15
Issue number5
DOIs
StatePublished - 12 Nov 2015

Keywords

  • Braid group
  • Commutator length
  • Concordance group
  • Conjugation invariant norm
  • Four ball genus
  • Quasimorphism

ASJC Scopus subject areas

  • Geometry and Topology

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