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VOL. 73 | 2017 On the recognition problem for virtually special cube complexes
Martin R. Bridson, Henry Wilton

Editor(s) Koji Fujiwara, Sadayoshi Kojima, Ken'ichi Ohshika

Abstract

We address the question of whether the property of being virtually special (in the sense of Haglund and Wise) is algorithmically decidable for finite, non-positively curved cube complexes. Our main theorem shows that it cannot be decided by examining one hyperplane at a time. Specifically, we prove that there does not exist an algorithm that, given a compact non-positively curved squared 2-complex $X$ and a hyperplane $H$ in $X$, will decide whether or not there is a finite-sheeted cover of $X$ in which no lift of $H$ self-osculates.

Information

Published: 1 January 2017
First available in Project Euclid: 4 October 2018

zbMATH: 07272044
MathSciNet: MR3728492

Digital Object Identifier: 10.2969/aspm/07310037

Subjects:
Primary: 20F10, 20F67, 57M07

Rights: Copyright © 2017 Mathematical Society of Japan

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