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On left-orderable fundamental groups and Dehn surgeries on knots. (English) Zbl 1419.57028

Summary: We show that the resulting manifold by \(r\)-surgery on a large class of two-bridge knots has left-orderable fundamental group if the slope \(r\) satisfies certain conditions. This result gives a supporting evidence to a conjecture of Boyer, Gordon and Watson [S. Boyer et al., Math. Ann. 356, No. 4, 1213–1245 (2013; Zbl 1279.57008)] that relates \(L\)-spaces and the left-orderability of their fundamental groups.

MSC:

57M27 Invariants of knots and \(3\)-manifolds (MSC2010)

Citations:

Zbl 1279.57008
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References:

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