On subsets of S^n whose (n + 1)-point subsets are contained in open hemispheres

Bieri, R., Kropholler, P. and Owens, B. (2014) On subsets of S^n whose (n + 1)-point subsets are contained in open hemispheres. New York Journal of Mathematics, 20, pp. 1021-1041.

Abstract

We investigate the nature of subsets of spheres which satisfy a tameness condition associated with the Bieri–Groves FPm-conjecture. We find that there is a natural polyhedrality in the case of n-tame subsets of an (n − 1)-sphere. In the case n = 3 we establish a strong polyhedrality condition for certain maximal open 3-tame sets. Many examples are included.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Owens, Professor Brendan and Kropholler, Prof Peter
• Authors: Bieri, R., Kropholler, P., and Owens, B.
• Subjects: Q Science > QA Mathematics
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: New York Journal of Mathematics
• Publisher: University at Albany
• ISSN: 1076-9803
• ISSN (Online): 1076-9803
• Copyright Holders: Copyright © 2014 The Authors
• First Published: First published in New York Journal of Mathematics 20:1021-1041
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher

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Project Code	Award No	Project Name	Principal Investigator	Funder's Name	Funder Ref	Lead Dept
56418	1	Alternating links and cobordism groups	Brendan Owens	Engineering & Physical Sciences Research Council (EPSRC)	EP/I033754/1	M&S - MATHEMATICS