Taut Foliations, Left-Orderability, and Cyclic Branched Covers

Boileau, M., Boyer, S.: Graph manifolds \(\mathbb {Z}\)-homology 3-spheres and taut foliations. arXiv:1303.5264 (2013) Boyer, S., Clay, A.: Foliations, orders, representations, L-spaces and graph manifolds. arXiv:1401.7726 (2014) Bludov, V.V., Glass, A.M.W.: Word problems, embeddings, and free products of right-ordered groups with amalgamated subgroup. Proc. Lond. Math. Soc.(3) 99(3), 585–608 (2009) Boyer, S., Gordon, C. M., Watson, L.: On L-spaces and left-orderable fundamental groups. Math. Ann. 356(4), 1213–1245 (2013) Boyer, S., Rolfsen, D., Wiest, B.: Orderable 3-manifold groups. Ann. Inst. Fourier (Grenoble) 55(1), 243–288 (2005) Boyer, S., Zhang, X.: Cyclic surgery and boundary slopes. Geometric topology (Athens, GA, 1993), AMS/IP Stud. Adv. Math., vol.2, Am. Math. Soc., Providence, RI, pp. 62–79 (1997) Calegari, D.: Foliations and the geometry of 3-manifolds. Oxford Mathematical Monographs. Oxford University Press, Oxford (2007) Calegari, D., Dunfield, N.M.: Laminations and groups of homeomorphisms of the circle. Invent. Math. 152(1), 149–204 (2003) Clay, A., Lidman, T., Watson, L.: Graph manifolds, left-orderability and amalgamation. Algebr. Geom. Topol. 13(4), 2347–2368 (2013) Dehornoy, P.: Braid groups and left distributive operations. Trans. Am. Math. Soc. 345(1), 115–150 (1994) Da̧bkowski, M.K., Przytycki, J. H., Togha, A.A.: Non-left-orderable 3-manifold groups. Canad. Math. Bull 48(1), 32–40 (2005) Eisenbud, D., Hirsch, U., Neumann, W.: Transverse foliations of Seifert bundles and self-homeomorphism of the circle. Comment. Math. Helv. 56(4), 638–660 (1981) Gabai, D.: Foliations and the topology of 3-manifolds. J. Differ. Geom. 18(3), 445–503 (1983) Gabai, D.: Foliations and the topology of 3-manifolds. III. J. Differ. Geom. 26(3), 479–536 (1987) Gordon, C. McA., Litherland, R.A.: Incompressible surfaces in branched coverings. The Smith conjecture (New York, 1979), Pure Appl. Math., Vol. 112, pp. 139–152. Academic, Orlando (1984) Greene, J.E.: Alternating links and left-orderability. arXiv:1107.5232 (2011) Hu, Y.: The left-orderability and the cyclic branched coverings. arXiv:1311.3291 (2013) Ito, T.: Non-left-orderable double branched coverings. Algebr. Geom. Topol. 13(4), 1937–1965 (2013) Jankins, M., Neumann, W.: Rotation numbers of products of circle homeomorphisms. Math. Ann. 271(3), 381–400 (1985) Kronheimer, P., Mrowka, T.: Witten’s conjecture and property P. Geom. Topol. 8, 2004. (electronic) Kronheimer, P., Mrowka, T., Ozsváth, P., Szabó, Z.: Monopoles and lens space surgeries. Annals Math. (2) 165(2), 457–546 (2007) Kazez, W.H., Roberts, R.: Approximating C 0 foliations. In press (2014) Kitano, T., Suzuki, M.: A partial order in the knot table. Experiment. Math. 14(4), 385–390 (2005) Kitano, T., Suzuki, M.: A partial order in the knot table II. Acta Math. Sin. (Engl. Ser.) 24(11), 1801–1816 (2008) Levine, A.S., Lewallen, S.: Strong L-spaces and left-orderability. Math. Res. Lett. 19, 2012 Lipshitz, R., Ozsváth, P., Thurston, D.: Bordered Heegaard Floer homology: Invariance and pairing. arXiv:0810.0687 (2008) Li, T., Roberts, R.: Taut foliations in knot complements. arXiv:1211.3066 (2012) Lisca, P., Stipsicz, A.I.: Ozsváth-Szabó invariants and tight contact 3-manifolds. III. J. Symplectic Geom. 5(4), 357–384 (2007) Morgan, J.W., Bass, H.: The Smith conjecture. Pure and applied mathematics Papers presented at the symposium held at Columbia University, Vol. 112. Academic, New York (1979) Minkus, J.: The branched cyclic coverings of 2 bridge knots and links. Mem. Am. Math. Soc. 35(255), iv+68 (1982) Meeks, W.I., Simon, L., Yau, S.T.: Embedded minimal surfaces, exotic spheres, and manifolds with positive Ricci curvature. Annals of Math. (2) 116(3), 621–659 (1982) Mulazzani, M., Vesnin, A.: The many faces of cyclic branched coverings of 2-bridge knots and links. Atti Sem. Mat. Fis. Univ. Modena. 49 suppl., 177–215 (2001). Dedicated to the memory of Professor M. Pezzana (Italian) Naimi, R.: Foliations transverse to fibers of Seifert manifolds. Comment. Math. Helv. 69(1), 155–162 (1994) Núñez, V., Ramir’ez-Losada, E.: The trefoil knot is as universal as it can be. Topol. Appl. 130(1), 1–17 (2003) Ozsváth, P., Szabó, Z.: Holomorphic disks and genus bounds. Geom. Topol. 8, 311–334 (2004) Ozsváth, P., Szabó, Z.: On knot Floer homology and lens space surgeries. Topology 44(6), 1281–1300 (2005) Ozsváth, P., Szabó, Z.: On the Heegaard Floer homology of branched double-covers. Adv. Math. 194(1), 1–33 (2005) Patton, R. M.: Incompressible punctured tori in the complements of alternating knots. Math. Ann. 301(1), 1–22 (1995) Peters, T.: On L-spaces and non left-orderable 3-manifold groups. arXiv:0903.4495 (2009) Roberts, R.: Constructing taut foliations. Comment. Math. Helv. 70(4), 516–545 (1995) Roberts, R.: Taut foliations in punctured surface bundles. I. Proc. Lond. Math. Soc.(3) 82(3), 747–768 (2001) Roberts, R.: Taut foliations in punctured surface bundles. II. Proc. London Math. Soc. (3) 83(2), 443–471 (2001) Teragaito, M.: Cyclic branched covers of alternating knots and L-spaces. arXiv:1404.6892 (2014) Teragaito, M.: Four-fold cyclic branched covers of genus one two-bridge knots are L-spaces To appear in Bol. Soc. Mat. Mexicana (2014) Tran, A.T.: On left-orderability and cyclic branched coverings. arXiv:1311.4262 (2013) Trotter, H.F.: Non-invertible knots exist. Topology 2, 275–280 (1963)