Non-left-orderable double branched coverings

Details Non-left-orderable double branched coverings Non-left-orderable double branched coverings

2011-06-08

arxiv.org/abs/1106.1499v3

Mathematics

Geometric Topology

20 Pages, 11 figures; Errors in Theorem 3 and 4 are corrected

Scientific paper

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

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