Vol. 292, No. 1, 2018

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ISSN: 0030-8730
The poset of rational cones

Joseph Gubeladze and Mateusz Michałek

Vol. 292 (2018), No. 1, 103–115
Abstract

We introduce a natural partial order on the set Cones(d) of rational cones in d. The poset of normal polytopes, studied by Bruns and the authors (Discrete Comput. Geom. 56:1 (2016), 181–215), embeds into Cones(d) via the homogenization map. The order in Cones(d) is conjecturally the inclusion order. We prove this for d = 3 and show a stronger version of the connectivity of Cones(d) for all d. Topological aspects of the conjecture are also discussed.

Keywords
rational cone, poset of cones, geometric realization of a poset
Mathematical Subject Classification 2010
Primary: 52B20
Secondary: 05E99, 20M13, 52C07
Milestones
Received: 14 June 2016
Revised: 29 May 2017
Accepted: 8 June 2017
Published: 22 September 2017
Authors
Joseph Gubeladze
Department of Mathematics
San Francisco State University
San Francisco, CA
United States
Mateusz Michałek
Freie Universität
Berlin
Germany
[3pt] Polish Academy of Sciences
Warsaw
Poland
Max-Planck-Institut für Mathematik in den Naturwissenschaften
Leipzig
Germany