### Abstract

Let n∈ Z^{+}. We provide two short proofs of the following classical fact, one using Khovanov homology and one using Heegaard–Floer homology: if the closure of an n-strand braid σ is the n-component unlink, then σ is the trivial braid.

Original language | English (US) |
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Title of host publication | Association for Women in Mathematics Series |

Publisher | Springer |

Pages | 93-101 |

Number of pages | 9 |

DOIs | |

State | Published - Jan 1 2016 |

### Publication series

Name | Association for Women in Mathematics Series |
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Volume | 6 |

ISSN (Print) | 2364-5733 |

ISSN (Electronic) | 2364-5741 |

### Keywords

- Braids
- Heegaard–floer homology
- Khovanov homology

### ASJC Scopus subject areas

- Mathematics(all)
- Gender Studies

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## Cite this

Grigsby, J. E., & Wehrli, S. M. (2016). An elementary fact about unlinked braid closures. In

*Association for Women in Mathematics Series*(pp. 93-101). (Association for Women in Mathematics Series; Vol. 6). Springer. https://doi.org/10.1007/978-3-319-34139-2_2