Representations of the (-2,3,7)-pretzel knot and orderability of Dehn surgeries

摘要

We construct a 1-parameter family of SL2(R) representations of the pretzel knot P(-2, 3, 7). As a consequence, we conclude that Dehn surgeries on this knot are left-orderable for all rational surgery slopes less than 6. Furthermore, we discuss a family of knots and exhibit similar orderability results for a few other examples. (C) 2021 Elsevier B.V. All rights reserved.