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Infinitesimal R ‐Trees Associated with Lifts of Quadratic Differentials without Connections in the Unit Disk
Author(s) -
SLUTSKIN LEV
Publication year - 1993
Publication title -
annals of the new york academy of sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.712
H-Index - 248
eISSN - 1749-6632
pISSN - 0077-8923
DOI - 10.1111/j.1749-6632.1993.tb52536.x
Subject(s) - infinitesimal , gravitational singularity , parameterized complexity , mathematics , tree (set theory) , unit disk , unit (ring theory) , topology (electrical circuits) , topological conjugacy , combinatorics , surface (topology) , space (punctuation) , pure mathematics , covering space , quadratic equation , geometry , mathematical analysis , computer science , mathematics education , operating system
It is shown that each pair of transverse measured foliations without connections between singularities on a compact surface contains within it a geometric structure that becomes an R ‐tree on the universal covering space. It is proved that the trees can be parameterized by sequences of positive numbers that reflect both their topological and geometric structures.