Papers and Preprints

What's new.

Published or publishing Papers

  1. Non-existence theorems on infinite order corks.(arXiv:1609.04344)(Adv. Math. 429(2023) Paper No. 109176)
  2. (with Tatsumasa Suzuki) Pochette surgery of S4 (arXiv:2205.06034)(accepted to PJM)
  3. Upsilon invariants of L-space cable knots (arXiv:1703.08828)(Topology and its applications 324 (2023) 108335, 25pp )
    (We give a Upsilon invariant formula of L-space cable knots.)
  4. The third term in lens surgery polynomials (Hiroshima Math. J. 51 (2021) no.1, 101--109)
  5. Boundary-sum irreducible finite order corks (Kobe Journal of Math 37 no. 1-2 (2020) pp.19--31) (arXiv:1710.07034)
    (The finite order corks in Finite order corks are boundary-sum irreducible.) We put the programs at this site.
  6. (with Youlin Li) Smoothly non-isotopic Lagrangian disk fillings of Legendrian knots Geom. Dedicata 213 (2021), 211-225)
  7. On the Alexander polynomial of lens space knots (Topol. App. Vol 275, 15(2020))(arXiv:1409.7032)
    This paper is a subsequent paper of "On a more constraint of knots yielding lens spaces". We prove the existence of the non-zero curve determined by non-zero coefficients on the plane. By using this we analyze the non-zero coefficients of Alexander polynomial of lens space knots.
  8. Homology spheres with E8-fillings and arbitrarily large correction terms (Indiana Univ. Math J. 70 (2021) no.3, 985--1002 )
    9. (arXiv:1811.11831)
  9. Notes on Gompf's infinite order corks  (Michigan Math. J. 70 (2021) 3- 21) (arXiv:1609.04345)
  10. Homology spheres yielding lens spaces (Proceedings of Gokova Geometry-Topology (2018) 73-121)
    We construct homology spheres yielding by Dehn surgery via simple (1,1)-knots in lens spaces
  11. (With Tetsuya Abe) Ribbon disks with the same exterior (Comm. Anal. Geom. Vol.30 No.2  257--270 　)
    12. (arXiv:1703.04913)
  12. (with Yuichi Yamada) Four dimensional manifolds constructed by lens space surgeries of distinct types (J. Knot Theory Ramifications 26 (2017), no. 11, 1750069)
  13. Finite order corks (Internat. J. Math Vol. 28 (2017) No. 6, pp.26)(arXiv:1601.07589)
    We show that there exist finite order corks with any order n.
  14. Heegaard Floer homology of Matsumoto's manifolds. (Adv. Math. vol. 320, 7(2017) 475-499) (arXiv:1504.08202)
    We compute Heegaard Floer homology of Matsumoto manifold and δ(D+(Ts,sp+1,n)) (s=2,3) and we give the necessary and sufficient condition for the double branched cover of D+(Ts,sp+1,n) to bound a rational homology 4-ball.
  15. The E8-boundings on homology spheres and negative sphere classes in E(1) (Topology Appl. 202 (2016) 160-182) (arXiv:1408.5528)
    We define topological invariants ds, ds, g8, g8 for a homology sphere. These invariants measure the sizes of bounding spin defeinite 4-manifolds. We construct E8-boundings for several Brieskorn homology spheres.
    Errata
  16. (with Tetsuya Abe.) A construction of slice knots via annulus twists (Michigan Math. J. vol. 65 no.3. (2016), 573-597) (arXiv:1305.7492)
    We constructed slice knots by using annulus twist.
  17. A plug with infinite order and some exotic 4-manifolds. (Journal of Gökova Geometry Topology, vol.9, (2015), 1-17) (arXiv:1201.6000 )
    In this paper I define a plug with infinite order and show an existence of mutually exotic 4-manifolds.
  18. (with Kouki Sato.) Non-orientable genus of a knot in punctured CP² (Tokyo J. Math. Vol.38, No.2, (2015,) 561-574) (arXiv:1403.1187)
    We define non-orientable minimal genus in nCP2 of a knot K. We show that the genus can take arbitrary large number.
  19. The link surgery of S² × S² and Scharlemann's manifolds (Hiroshima Math. J. 44 (2014), no.1, 35-62) (arXiv:1011.5308)
    Akaho's manifolds and Scharlemann's manifods are standard. Classification of link surgery operation of S2× S2.
  20. On Nash's 4-sphere and Property 2R (Turkish J. Math. 37 (2013), no. 2, 360-374.)
    D. Nash constructed a family of homotopy 4-sphere. The paper shows that they are all standard. We give a new potential counterexample of generalized Property R conjecture. Actually, these are not counterexamples.
  21. (with Yuichi Yamada) Four dimensional manifolds constructed by lens space surgeries along torus knots (J. Knot Theory Ramifications 21 (2012) no.11)
    We classify the torus-knot pairs T(a,b),T(c,d) such that M(T(a,b),p)=±M(T(c,d),p) is a lens space. and X(T(a,b),p)∪X(T(c,d),p) are all standard 4-manifolds.
  22. On the non-existence of L-space surgery structure (Osaka J. Math. 48 (2011) no.2, 541-547)
    The Poincare homology sphere with reversed orientation does not contain any knot yielding lens spaces by positive integral Dehn surgery.
  23. Remarks on lens space surgery (Kobe J. Math. 26(2009) 47-58)
    We show that lens space L(*,q) with Dehn surgery of S3 is finite if and only if q is a non-square number. We also partially solve Teragaito's conjecture, The Ozsvath-Szabo's correction term of lens space coincides with Fukumoto and Furuta's w-invariant. This coincidence has been shown by M. Ue recently.
  24. Lens spaces given from L-space homology spheres (Experiment. Math. 18(2009), no. 3, 285-301)
  25. Ozsváth-Szabó's correction term and lens surgery (Math. Pro. Cambridge Philos. Soc. 146(2009), no 01, pp. 119-134)
  26. On applications of correction term to lens space (Intelligence of low dimensional topology 2006, 315-322, Ser. Knots Everything, 40, World Sci. Publ., Hackensack, NJ, 2007)
  27. A 2-knot connected-sum and 4-dimensional diffeomorphism (J. Math. Kyoto Univ. 46(2006), no.4 879-890)
  28. On the diffeomorphisms for Akbulut's knot concordance surgery (J. Knot Theory Ramifications 14 (2005), no. 5, 539-564 )

 

RIMS Kokyuroku

  1. Omae's knot and 12a990 are ribbon (written by T. Abe)
    (Proceeding of Intelligence of Low-dimensional Topology at RIMS 2013)
    Omae's knot is ribbon in the n=1 case. and 12a990 is also ribbon.
  2. Introduction to Heegaard Floer homology
    (Proceeding to Intelligence of Low-dimensional Topology at RIMS 2016)
    Overview of Heegaard Floer homology

Proceedings

  1. On a diffeomorphism of knot surgery by Akbulut (Japanese)
    (Proceeding of 50th Topology simposium 2003, Matsumoto)
  2. On the Dehn surgery realization problem on lens space (Japanese)
    (Proceeding of 58th Topology simposium 2011, University of Tsukuba)

Preprints

(These are the latest version.)

  1. On a more constraint of knots yielding lens spaces
    (This is the older version of "The Alexander polynomial of lens space knot".) unsubmitted
    The second term of Alexander polynomial of knot yielding lens space is -1. The non-zero coeffieicnts 1,-1 are adjacent in some region. Bounded below of the Seifert genus of knot admitting lens surgery is shown.
  2. A complete list of lens spaces constructed by Dehn surgery I (arXiv:1005.3512)
    As long as any lens space surgery which τ is greater than 1, Berge's list is complete. The invariant τ is a non-negative integer valued invariant concerning lens space surgery.
  3. Variations of 4-dimensional twists obtained by an infinite order plug(arXiv:1508.03092)
    We give exotic 2-handle attachments of an infinite order plug and variations of infinite order plug.

In preparation

  1. Rational 4-ball and branched double cover.
    If the double covoer along D+(T(s,sp+1),n) bounds a rational 4-ball, then (s,p,n)=(m,1,m(m+1)), (2,3,12),(3,2,20),(6,3,110) only. The first one is a forklore, second and third ones are in "Heegaard Floer homology of Matsumoto's manifolds".

Master Thesis

Doctor Thesis

Japanese Book

Some calculus


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