Fundamental Groups, Slalom Curves and Extremal Length

Chapter
Part of the Operator Theory: Advances and Applications book series (OT, volume 261)

Abstract

We define two versions of the extremal length of elements of the fundamental group of the twice punctured complex plane and give upper and lower bounds for two versions of this invariant. The bounds differ by a multiplicative constant. The main motivation comes from 3-braid invariants and their application.

Keywords

Fundamental group extremal length conformal module 3-braids 

Mathematics Subject Classification (2010)

Primary 30Cxx Secondary 20F34 20F36 57Mxx 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institut für MathematikHumboldt-University BerlinBerlinGermany

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