We develop a method to compute the genera and slopes of essential surfaces in 2-bridge link exteriors with one longitudinal boundary component. The tools we use are those developed by Floyd and Hatcher in [4]. Such computations allow us to compute the genera of satellite tunnel number one knots and torti-rational knots.
[1] G. Burde and H. Zieschang: Knots, de Gruyter Studies in Mathematics 5, Walter de Gruyter & Co., Berlin, 1985.
[2] M. Eudave-Munoz, F. Manjarrez-Gutierrez and E. Ramirez-Losada: Classification of genus two knots which admit a (1,1)-decomposition, Topology Appl.230 (2017), 468-489.
[3] M. Eudave-Munoz: On nonsimple 3-manifolds and 2-handle addition, Topology Appl.55 (1994),131-152.
[4] W. Floyd and A. Hatcher: The space of incompressible surfaces in a 2-bridge link complement, Trans. Amer. Math. Soc. 305 (1988), 575-599.
[5] H. Goda, C. Hayashi, and H.J. Song: Dehn surgeries on 2- bridge links which yield reducible 3-manifolds, J. Knot Theory Ramifications 18 (2009), 917-956.
[6] M. Hirasawa and K. Murasugi: Fibered torti-rational knots, J. Knot Theory Ramifications 19 (2010), 1291-1353.
[7] J. Hoste and P.D. Shanahan: Computing boundary slopes of 2-bridge links, Math. Comp., 76 (2007),1521- 1545.
[8] A.E. Lash: Boundary curve space of the Whitehead link complement, Ph.D. Thesis, University of Califor nia, Santa Barbara, 1993.
[9] H. Matsuda: Genus one knots which admit (1,1)-decompositons, Proc. Amer. Math. Soc.130 (2002), 2155-2163.
[10] K. Morimoto and M. Sakuma: On unknotting tunnels for knots, Math. Ann. 289 (1991),143-167.
[11] E. Ramirez-Losada and L.G. Valdez-Sanchez: Crosscap number two knots inS3 with (1,1)decompositions, Bol. Soc. Mat. Mexicana, Tercera Serie 10 (2004), 451465.
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