Polyhedral Horofunction Compactification as a Polyhedral Ball
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2016
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| _version_ | 1866909193976414208 |
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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 |