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Non-left-orderable double branched coverings

Tetsuya Ito
Algebraic & Geometric Topology 13 (2013) 1937–1965
DOI: 10.2140/agt.2013.13.1937
Abstract

We develop a method to show the fundamental group of the double branched covering of links is not left-orderable by introducing a notion of coarse presentation. Like usual group presentations, a coarse presentation is given by a set of generators and relations, but inequalities are allowed as relations. By using coarse presentations, we give a family of links whose double branched covering has non-left-orderable fundamental group. Our family of links includes many known and new examples.

Keywords
left-orderable groups, coarse presentation, double branched coverings, L–space
Mathematical Subject Classification 2010
Primary: 57M05
Secondary: 57M12, 57M27
References
Publication
Received: 13 April 2012
Revised: 14 February 2013
Accepted: 16 February 2013
Published: 24 May 2013
Authors
Tetsuya Ito
Research Institute for Mathematical Sciences
Kyoto University
Sakyo-ku, Kyoto 606-8502
Japan
http://www.kurims.kyoto-u.ac.jp/~tetitoh/