과제정보
This work was supported by a 2-Year Research Grant of Pusan National University.
참고문헌
- H. Aydin, I. Gultekyn and M. Mulazzani, Torus knots and Dunwoody manifolds, Siberian Math. J. 45 (2004), no. 1, 1-6. https://doi.org/10.1023/b:simj.0000013008.25556.29
- S. A. Bleiler, Two-generator cable knots are tunnel one, Proc. Amer. Math. Soc. 122 (1994), no. 4, 1285-1287. https://doi.org/10.2307/2161200
- G. Burde and H. Zieschang, Knots, de Gruyter Studies in Mathematics 5. Walter de Gruyter, Berlin, 1985.
- A. Cattabriga and M. Mulazzani, All strongly-cyclic branched coverings of (1, 1)-knots are Dunwoody manifolds, J. London Math. Soc. 70 (2004), no. 2, 512-528. https://doi.org/10.1112/S0024610704005538
- H. R. Cho, S. Y. Lee and H.-J. Song, Derivations of Schubert normal forms of 2-bridge knots from (1, 1)-diagrams, J. Knot Theory Ramifications 28 (2019), no. 8, 1950048 (29 pages). https://doi.org/10.1142/S0218216519500482
- M. J. Dunwoody, Cyclic presentations and 3-manifolds, in Proc. Inter. Conf., Groups-Korea 94. Walter de Gruyter, Berlin-New York (1995), 47-55.
- H. Doll, A genralized bridge number for links in 3-manifolds, Math. Ann. 294 (1992), no. 1, 701-717. https://doi.org/10.1007/BF01934349
- L. Grasselli and M. Mulazzani, Genus one 1-bridge knots and Dunwoody manifolds, Forum Math. 13 (2001), no. 3, 379-397.
- C. Hayashi, 1-genus 1-bridge splittings for knots, Osaka J. Math. 41 (2004), no. 2, 371-426.
- G. Kim and S. Y. Lee, Doubly-pointed Heegaard diagrams of (1, 1)-knots up to 10 crossings and (1, 1)-pretzel knots, preprint (2021).
- E. Klimenko and M. Sakuma, Two-generator discrete subgroups of Isom(H2) containing orientation-reversing elements, Geom. Dedicata 72 (1998), 247-282. https://doi.org/10.1023/A:1005032526329
- K. Morimoto and M. Sakuma, On unknotting tunnels for knots, Math. Ann. 289 (1991), no. 1, 143-167. https://doi.org/10.1007/BF01446565
- K. Morimoto, M. Sakuma and Y. Yokota, Identifying tunnel number one knots, J. of the Mathematical Society of Japan 48 (1996), no. 4, 667-688. https://doi.org/10.2969/jmsj/04840667
- Mario Eudave Muoz, On nonsimple 3-manifolds and 2-handle addition, Topology Appl. 55 (1994), no. 2, 131-152. https://doi.org/10.1016/0166-8641(94)90114-7
- D. Rolfsen, Knots and links, Mathematics Lecture Series 7, Publish or Perish, Inc., Berkeley, 1976.