Alexander polynomial obstruction of bi-orderability for rationally homologically fibered knot groups

Abstract

We show that if the fundamental group of the complement of a rationally homologically fibered knot in a rational homology 3-sphere is bi-orderable, then its Alexander polynomial has at least one positive real root. Our argument can be applied for a finitely generated group which is an HNN extension with certain properties.

5 pages, no figures. Title was changed since our argument requires the rationally homologically fibered conditions

References in corpus (1)

• Residual nilpotence and ordering in one-relator groups and knot groups

Cited by in corpus (4)

• Generalized torsion and Dehn filling
• Ordered bases, order-preserving automorphisms and bi-orderable link groups
• Generalized torsion orders of generalized torsion elements
• Generalized torsion for hyperbolic $3$--manifold groups with arbitrary large rank