Polyhedral Horofunction Compactification as a Polyhedral Ball

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Hauptverfasser: Ji, Lizhen, Schilling, Anna-Sofie
Format: Preprint
Veröffentlicht: 2016
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author Ji, Lizhen
Schilling, Anna-Sofie
author_facet Ji, Lizhen
Schilling, Anna-Sofie
contents In this paper we answer positively a question raised by Kapovich and Leeb in a paper titled "Finsler bordifications of symmetric and certain locally symmetric spaces". Specifically, we show that for a finite-dimensional vector space with a polyhedral norm, its horofunction compactification is homeomorphic to the dual unit ball of the norm by an explicit map. To prove this, we establish a criterion for converging sequences in the horofunction compactification and generalize the basic notion of the moment map in the theory of toric varieties.
format Preprint
id arxiv_https___arxiv_org_abs_1607_00564
institution arXiv
publishDate 2016
record_format arxiv
spellingShingle Polyhedral Horofunction Compactification as a Polyhedral Ball
Ji, Lizhen
Schilling, Anna-Sofie
Geometric Topology
Metric Geometry
In this paper we answer positively a question raised by Kapovich and Leeb in a paper titled "Finsler bordifications of symmetric and certain locally symmetric spaces". Specifically, we show that for a finite-dimensional vector space with a polyhedral norm, its horofunction compactification is homeomorphic to the dual unit ball of the norm by an explicit map. To prove this, we establish a criterion for converging sequences in the horofunction compactification and generalize the basic notion of the moment map in the theory of toric varieties.
title Polyhedral Horofunction Compactification as a Polyhedral Ball
topic Geometric Topology
Metric Geometry
url https://arxiv.org/abs/1607.00564