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  Fundamental groups, 3-braids, and effective estimates of invariants

Jöricke, B. (2020). Fundamental groups, 3-braids, and effective estimates of invariants. Mathematische Zeitschrift, 294(3-4), 1553-1609. doi:10.1007/s00209-019-02317-6.

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Item Permalink: https://hdl.handle.net/21.11116/0000-0006-0C44-1 Version Permalink: https://hdl.handle.net/21.11116/0000-000E-1259-A
Genre: Journal Article

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 Creators:
Jöricke, Burglind1, Author           
Affiliations:
1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

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Free keywords: Mathematics, Geometric Topology, Mathematics, Complex Variables
 Abstract: We define invariants of braids rather than invariants of conjugacy classes of braids. For any pure three-braid we give effective upper and lower bounds for these invariants. This is done in terms of a natural syllable decomposition of the word representing the image of the braid in the braid group modulo its center. The bounds differ by a multiplicative constant not depending on the word. Respective bounds are given for all three-braids. We also obtain effective upper and lower bounds for the entropy of pure three-braids in these terms. The proof leads to the study of the extremal length of classes of curves
representing elements of the fundamental group of the twice punctured complex plane.

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Language(s): eng - English
 Dates: 2020
 Publication Status: Issued
 Pages: 57
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 Table of Contents: -
 Rev. Type: Peer
 Identifiers: arXiv: 1712.10307
DOI: 10.1007/s00209-019-02317-6
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Title: Mathematische Zeitschrift
  Abbreviation : Math. Z.
Source Genre: Journal
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Publ. Info: Springer
Pages: - Volume / Issue: 294 (3-4) Sequence Number: - Start / End Page: 1553 - 1609 Identifier: -