Classical pretzel knots and left orderability

Abstract

We consider the classical pretzel knots [Formula: see text], where [Formula: see text] are positive odd integers. By using continuous paths of elliptic [Formula: see text]-representations, we show that (i) the 3-manifold obtained by [Formula: see text]-surgery on [Formula: see text] has left orderable fundamental group if [Formula: see text] and (ii) the [Formula: see text]-cyclic branched cover of [Formula: see text] has left orderable fundamental group if [Formula: see text].