Fundamental Groups, Slalom Curves and Extremal Length
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.
KeywordsFundamental group extremal length conformal module 3-braids
Mathematics Subject Classification (2010)Primary 30Cxx Secondary 20F34 20F36 57Mxx
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