@inproceedings{c9a4e0aa90cc4dcf9333bd55d90a2f40,
title = "Realization Spaces of Arrangements of Convex Bodies",
abstract = "We introduce combinatorial types of arrangements of convex bodies, extending order types of point sets to arrangements of convex bodies, and study their realization spaces. Our main results witness a trade-off between the combinatorial complexity of the bodies and the topological complexity of their realization space. On one hand, we show that every combinatorial type can be realized by an arrangement of convex bodies and (under mild assumptions) its realization space is contractible. On the other hand, we prove a universality theorem that says that the restriction of the realization space to arrangements of convex polygons with a bounded number of vertices can have the homotopy type of any primary semialgebraic set.",
keywords = "Convex sets, Mnev s universality theorem, Oriented matroids, Realization spaces",
author = "Dobbins, \{Michael Gene\} and Andreas Holmsen and Alfredo Hubard",
year = "2015",
month = jun,
day = "1",
doi = "10.4230/LIPIcs.SOCG.2015.599",
language = "English",
series = "Leibniz International Proceedings in Informatics, LIPIcs",
publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",
pages = "599--614",
editor = "Janos Pach and Lars Arge",
booktitle = "31st International Symposium on Computational Geometry, SoCG 2015",
note = "31st International Symposium on Computational Geometry, SoCG 2015 ; Conference date: 22-06-2015 Through 25-06-2015",
}