Paper

  1. Uniqueness of essential free tangle decompositions of knots and links, KNOTS '96 (Tokyo), 231--238, World Sci. Publishing, River Edge, NJ, 1997.
  2. On uniqueness of essential tangle decompositions of knots with free tangle decompositions, in Proc. Appl. Math. Workshop 8, ed. G. T. Jin and K. H. Ko, KAIST, Taejon (1998) 227-232.
  3. Free genus one knots do not admit essential tangle decompositions, J. Knot Theory Ramifications 7 (1998), no. 7, 945--953. (with Hiroshi Matsuda)
  4. Satellite knots of free genus one, J. Knot Theory Ramifications 8 (1999), no. 1, 27--31.
  5. On tangle decompositions of tunnel number one links, J. Knot Theory Ramifications 8 (1999), no. 3, 299--320. (with Hiroshi Goda and Masakazu Teragaito)
  6. Genus one, three-bridge knots are pretzel, J. Knot Theory Ramifications 8 (1999), no. 7, 879--885. (with Satoshi Fukuhama and Masakazu Teragaito)
  7. Tangle decompositions of satellite knots, Rev. Mat. Complut. 12 (1999), no. 2, 417--437. (with Chuichiro Hayashi and Hiroshi Matsuda)
  8. Tangle decompositions of double torus knots and links, J. Knot Theory Ramifications 8 (1999), no. 7, 931--939.
  9. Synchronism of an incompressible non-free Seifert surface for a knot and an algebraically split closed surface in the knot complement, Proc. Amer. Math. Soc. 128 (2000), no. 3, 919--922.
  10. Hyperbolic knot complements without closed embedded totally geodesic surfaces, J. Austral. Math. Soc. Ser. A 68 (2000), no. 3, 379--386. (with Kazuhiro Ichihara)
  11. Accidental surfaces in knot complements, J. Knot Theory and its Ramifications 9 (2000), no. 6, 725--733. (with Kazuhiro Ichihara)
  12. Satellite double torus knots, J. Knot Theory and its Ramifications 10 (2001), no. 1, 133--142.
  13. Additivity of free genus of knots, Topology 40 (2001), 659-665.
  14. Impossibility of obtaining split links from split links via twistings, J. Knot Theory and its Ramifications 10 (2001), no. 8, 1229--1231.
  15. Accidental surfaces and exceptional surgeries, Osaka J. Math. 39 (2002), 335--343 (with Kazuhiro Ichihara)
  16. On non-simple reflexive links, J. Knot Theory and its Ramifications 11 (2002) 787--791. (with Hiroshi Matsuda and Koya Shimokawa)
  17. Closed incompressible surfaces in the complements of positive knots, Comment. Math. Helv. 77 (2002) 235--243.
  18. Totally knotted Seifert surfaces with accidental peripherals, Proc. Amer. Math. Soc. 131 (2003) 3945--3954. (with Yukihiro Tsutsumi)
  19. Minimally knotted spatial graphs are totally knotted, Tokyo J. Math. 26 (2003) 413--421. (with Yukihiro Tsutsumi)
  20. Newly found forbidden graphs for trivializability, J. Knot Theory and its Ramifications 14 (2005) 523--538 (with Ryo Nikkuni, Kouki Taniyama and Yukihiro Tsutsumi)
  21. Non-triviality of generalized alternating knots, J. Knot Theory and its Ramifications 15 (2006) 351--360.
  22. Primitive spatial graphs and graph minors, Rev. Mat. Complut. 20 (2007), no. 2, 391--406. (with Yukihiro Tsutsumi)
  23. Morse position of knots and closed incompressible surfaces, J. Knot Theory and its Ramifications 17 (2008) 377--397.
  24. On a genus of a closed surface containing a Brunnian link, Tokyo J. Math. 31 (2008) 347--349.
  25. Closed incompressible surfaces of genus two in 3-bridge knot complements, Topology and its Appl. 156 (2009) 1130--1139.
  26. Ascending number of knots and links, J. Knot Theory and its Ramifications 19 (2010) 15--25.
  27. Waist and trunk of knots, Geometriae Dedicata 149 (2010) 85--94.
  28. Rational structure on algebraic tangles and closed incompressible surfaces in the complements of algebraically alternating knots and links, Topology and its Applications 157 (2010) 1937--1948.
  29. Essential state surfaces for knots and links, J. Austral. Math. Soc. 91 (2011) 391--404.
  30. Non-minimal bridge positions of torus knots are stabilized, Math. Proc. Cambridge Philos. Soc. 151 (2011) 307--317.
  31. Bridge position and the representativity of spatial graphs, Topology and its Appl. 159 (2012) 936--947.
  32. The representativity of pretzel knots, J. Knot Theory and its Ramifications 21, 1250016 (2012).
  33. On the Neuwirth conjecture for knots, Communications in Analysis and Geometry 20 (2012) 1019-1060. (with J. Hyam Rubinstein)
  34. A locally minimal, but not globally minimal bridge position of a knot, Math. Proc. Cambridge Philos. Soc. 155 (2013) 181--190. (with Kazuto Takao)
  35. Essential surfaces of non-negative Euler characteristic in genus two handlebody exteriors, Trans. Amer. Math. Soc. 367 (2015) 2875-2904 (with Yuya Koda, with an appendix by Cameron Gordon)
  36. Knotted handle decomposing spheres for handlebody-knots, J. Math. Soc. Japan. 67 (2015) 407--417. (with Atsushi Ishii and Kengo Kishimoto)
  37. Composite tunnel number one genus two handlebody-knots, Bol. Soc. Mat. Mexicana 20 (2014) 375--390. (with Mario Eudave-Munoz)
  38. Coexistence of coiled surfaces and spanning surfaces for knots and links, J. Austral. Math. Soc. 99 (2015) 250--259.
  39. Musubime to Kyokumen, Math. Soc. Japan, Sugaku Vol. 67, No. 4 (2015) 403--423. (Japanese Survey)
  40. Knot homotopy in subspaces of the 3-sphere, Pacific J. Math. 282 (2016) 389--414. (with Yuya Koda)
  41. An obstruction to embedding 2-dimensional complexes into the 3-sphere, Topology and its Appl. 198 (2016) 117--125. (with Kazufumi Eto, Shosaku Matsuzaki)
  42. A knot with destabilized bridge spheres of arbitrarily high bridge number, J. London Math. Soc. 93 (2016) 379--396. (with Yeonhee Jang, Tsuyoshi Kobayashi, Kazuto Takao)
  43. Dehn surgery and Seifert surface system, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) Vol. XVII (2017) 267--276. (with Koya Shimokawa)
  44. Genera and minors of multibranched surfaces, Topology and its Appl. 230 (2017) 621--638. (with Shosaku Matsuzaki)
  45. Unknotting submanifolds of the 3-sphere by twistings, Ann. Sc. Norm. Super. Pisa Cl. Sci. (3) Vol. XVIII (2018) 1145--1153.
  46. A note on the paper "A knot with destabilized bridge spheres of arbitrarily high bridge number", RIMS K?ky?roku 2099 (2019) 89--104. (with Yeonhee Jang, Tsuyoshi Kobayashi, Kazuto Takao)
  47. Decomposing Heegaard splittings along separating incompressible surfaces in 3-manifolds, Topology and its Appl. 264 (2019) 21--26. (with Kazuhiro Ichihara and J. Hyam Rubinstein)
  48. Characterization of 3-punctured spheres in non-hyperbolic link exteriors, Topology and its Appl. 264 (2019) 300--312. (with Mario Eudave-Munoz)
  49. Two More Proofs that the Kinoshita Graph is Knotted, Amer. Math. Monthly 126 (2019) 352--357. (with Scott Taylor)
  50. Height, trunk and representativity of knots, J. Math. Soc. Japan. 71 (2019) 1105--1121. (with Ryan Blair)
  51. Neighborhood equivalence for multibranched surfaces in 3-manifolds, Topology and its Appl. 257 (2019) 11--21. (with Kai Ishihara, Yuya Koda, Koya Shimokawa)
  52. The incompatibility of crossing number and bridge number for knot diagrams, Discrete Mathematics 342 (2019) 1966--1978. (with Ryan Blair, Alexandra Kjuchukova)
  53. Knots and surfaces, Amer. Math. Soc. Sugaku Expositions 32 (2019) 155--179. (English translation of Japanese article "Musubime to Kyokumen", Math. Soc. Japan, Sugaku Vol. 67, No. 4 (2015) 403--423.)
  54. Stabilization of bridge decompositions of knots and bridge positions of knot types, RIMS K?ky?roku 2135 (2019). (with Yeonhee Jang, Tsuyoshi Kobayashi, Kazuto Takao)
  55. A partial order on multibranched surfaces in 3-manifolds, Topology and its Appl. 272 (2020) 107074.
  56. The maximum and minimum genus of a multibranched surface, Topology and its Appl. 301 (2020) 107502. (with Mario Eudave-Munoz)
  57. Multibranched surfaces in 3-manifolds, Zapiski Nauchnykh Seminarov POMI, 498 (2020) 135--156. (Survey)
  58. Multibranched Surfaces in 3-Manifolds, J. Math. Sci. 255 (2021) 193--208. (English version of volume 498 of "Zapiski Nauchnykh Seminarov POMI")
  59. Stable equivalence of bridge positions of a handlebody-knot, International Journal of Mathematics 32 (2021) 2150093.
  60. Handlebody decompositions of 3-manifolds and polycontinuous patterns, Proceedings of the Royal Society A. 478 (2022) 20220073. (with Naoki Sakata, Ryosuke Mishina, Masaki Ogawa, Kai Ishihara, Yuya Koda, Koya Shimokawa)
  61. Essential annuli in genus two handlebody exteriors, to appear in Algebraic & Geometric Topology. (with Yuya Koda, Yi-Sheng Wang)

In submission or preparation

  1. Forbidden complexes for the 3-sphere, arXiv:2403.18279. (with Mario Eudave-Munoz)
  2. On symmetry and exterior problems of knotted handlebodies, arXiv:2506.06713. (with Yuya Koda, Yi-Sheng Wang)
  3. Tritangle decompositions of genus two handlebody-knots. (with Yi-Sheng Wang)

Almost all preprints are downloadable at Advanced Search | arXiv e-print repository.

Article

  1. 結び目と曲面, 数学セミナー 2018年7月号, 13--19.
  2. 結び目と曲面, 祝祷 文化講演集 第19輯, 駒澤大学 (2018) 69--76.
  3. アレクサンダーの角付き球面, 数学セミナー 2019年11月号, 83.

Unpublished

  1. Thin position for incompressible surfaces in 3-manifolds. (with Kazuhiro Ichihara and J. Hyam Rubinstein)
  2. Edge number of knots and links
  3. A property of diagrams of the trivial knot
  4. Uniqueness of primitive embeddings of the Petersen graph
  5. Complexity of embeddings of a graph into the $3$-sphere
  6. Forbidden minors for apex graphs
  7. Tangle decompositions of knots and links
  8. Thin position of manifolds
  9. Essential free decompositions of knot exteriors
  10. Interpolating manifolds for knots
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