Non-left-orderable double branched coverings

Abstract

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.

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

References in corpus (2)

• On L-spaces and non left-orderable 3-manifold groups
• On L-spaces and left-orderable fundamental groups

Cited by in corpus (6)

• Left-orderability and cyclic branched coverings
• On L-spaces and left-orderable fundamental groups
• Non-left-orderability of cyclic branched covers of pretzel knots $P(3,-3,-2k-1)$
• Taut foliations, left-orderability, and cyclic branched covers
• Left-orderable, non-L-space surgeries on knots
• Genus one open books with non-left-orderable fundamental group