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- Title
Classical pretzel knots and left orderability.
- Authors
Khan, Arafat; Tran, Anh T.
- Abstract
We consider the classical pretzel knots P (a 1 , a 2 , a 3) , where a 1 , a 2 , a 3 are positive odd integers. By using continuous paths of elliptic SL 2 (ℝ) -representations, we show that (i) the 3-manifold obtained by m l -surgery on P (a 1 , a 2 , a 3) has left orderable fundamental group if m l < 1 and (ii) the n th -cyclic branched cover of P (a 1 , a 2 , a 3) has left orderable fundamental group if n > 2 π / arccos (1 − 2 / (1 + a 1 a 2 + a 2 a 3 + a 3 a 1)).
- Subjects
PRETZELS; FUNDAMENTAL groups (Mathematics); INTEGERS
- Publication
International Journal of Mathematics, 2021, Vol 32, Issue 11, p1
- ISSN
0129-167X
- Publication type
Article
- DOI
10.1142/S0129167X21500804