New York Journal of Mathematics
Volume 23 (2017) 497-503


Tetsuya Ito

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

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Published: April 4, 2017
Keywords: Bi-orderable group, Alexander polynomial
Subject: Primary~57M05, Secondary~20F60,06F15

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.


This work was supported by JSPS KAKENHI Grant Number 15K17540.

Author information

Department of Mathematics, Graduate School of Science, Osaka University, 1-1 Machikaneyama Toyonaka, Osaka 560-0043, JAPAN