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Abstract
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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.
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Keywords
left-orderable groups, coarse presentation, double branched
coverings, L–space
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Mathematical Subject Classification 2010
Primary: 57M05
Secondary: 57M12, 57M27
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Publication
Received: 13 April 2012
Revised: 14 February 2013
Accepted: 16 February 2013
Published: 24 May 2013
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