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.

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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, Dr 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 CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
564181Alternating links and cobordism groupsBrendan OwensEngineering & Physical Sciences Research Council (EPSRC)EP/I033754/1M&S - MATHEMATICS