The Metric Completion of Outer Space

Details The Metric Completion of Outer Space The Metric Completion of Outer Space

2012-02-28

arxiv.org/abs/1202.6392v1

Mathematics

Group Theory

Scientific paper

We prove that the completion of Outer Space with the Lipschitz metric is
homeomorphic to the free splitting complex. We give a new proof of a theorem by
Francaviglia and Martino [FMa] that the isometry group of Outer Space is
homeomorphic to Out(F_n) for n \geq 3 and equal to PSL(2,\ZZ) for n = 2.

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