The metric completion of Outer Space

Yael Algom-Kfir

doi:10.1007/s10711-019-00451-3

The metric completion of Outer Space

Yael Algom-Kfir

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We develop the theory of a metric completion of an asymmetric metric space. We characterize the points on the boundary of Outer Space that are in the metric completion of Outer Space with the Lipschitz metric. We prove that the simplicial completion, the subset of the completion consisting of simplicial tree actions, is homeomorphic to the free splitting complex. We use this to give a new proof of a theorem by Francaviglia and Martino that the isometry group of Outer Space is isomorphic to Out (F_n) for n≥ 3 and to PSL (2 , Z) for n= 2.

Original language	English
Pages (from-to)	191-230
Number of pages	40
Journal	Geometriae Dedicata
Volume	204
Issue number	1
DOIs	https://doi.org/10.1007/s10711-019-00451-3
State	Published - 1 Feb 2020

Bibliographical note

Publisher Copyright:
© 2019, Springer Nature B.V.

Keywords

Asymmetric metric space
Metric completion
Out(F)
Outer Space
Quasimetric space

ASJC Scopus subject areas

Geometry and Topology

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10.1007/s10711-019-00451-3

Cite this

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The metric completion of Outer Space

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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