Infinite family of non-left-orderable L-spaces

For each connected alternating tangle, we provide an infinite family of non-left-orderable L-spaces. This gives further support for Conjecture [3] of Boyer, Gordon, and Watson that is a rational homology 3-sphere is an L-space if and only if it is non-left-orderable. These 3-manifolds are obtained as Dehn fillings of the double branched covering of any alternating encircled tangle. We give a presentation of these non-left-orderable L-spaces as double branched coverings of S3 , branched over some specified links that turn out to be hyperbolic. We show that the obtained families include many Seifert fibered spaces. We also give a surgery description for some of them. In the process we give another way to prove that the torus knots T (2, 2m + 1) are L-space-knots as has already been shown by Ozsv\'ath and Szab\'o in [19].