My Works

Reserch Papers (November 9, 2020)

  1. On transversely flat conformal foliations with good measures, Trans. Amer. Soc. 348 (1996), 1939-1958.
  2. Classification of Riemannian flows with transverse similarity structures, Ann. Fac. Sci. Toulouse Vol.VI, no.2 (1997), 203-227.
  3. Invariance of the Godbillon-Vey class by C1-diffeomorphisms for higher codimensional foliations, Jour. Math. Soc. Japan Vol.51, No.3 (1999), 655-660.
  4. On transversely flat conformal foliations with good measures II, Hiroshima Math. Jour. Vol.28, No.3 (1998), 523-525.
  5. On the Real Secondary classes of transversely holomorphic foliations, Ann. Inst. Fourier, Vol.50, No.3 (2000), 995-1017.
  6. On the real secondary classes of transversely holomorphic foliations II, Tôhoku Math. J. 55 (2003), 361-374.
  7. A Remark on the Bott class, Ann. Fac. Sci. Toulouse Vol. X, no.1 (2001), 5-21.
  8. Localization and Residue of the Bott class, Topology, Vol.43 (2004), 289-317.
  9. Complexification of foliations and Complex secondary classes, Bull. Braz. Math. Soc, NS Vol.34, No.2 (2003), 251-262.
  10. Residues of the Bott class and an application to the Futaki invariant, Asian J. Math., Vol.7, No.2 (2003), 239-268.
  11. On Quasiconformal Deformations of Transversely Holomorphic Foliations, Jour. Math. Soc. Japan, Vol. 57, No.3 (2005), 725-734.
  12. Infinitesimal derivative of the Bott class and the Schwarzian derivatives, Tohoku Math. J., Vol.61 (2009), 393-416.
  13. A Fatou-Julia decomposition of transversally holomorphic foliations, Ann. Inst. Fourier (Grenoble), Vol. 60 (2010), 1057-1104.
  14. On Fatou-Julia decompositions, Ann. Fac. Sci. Toulouse, Vol. 22 (2013), 155-195.
  15. On independent rigid classes in H*(WUq), Illinois J. of Math., Vol. 56 (2012), 1001-1343 (actually appeared in 2014).
  16. Transverse projective structures of foliations and infinitesimal derivatives of the Godbillon-Vey class, Internat. J. Math., Vol.26 (2015), 1540001, 29pp, Shoshichi Kobayashi Memorial Volume
  17. Derivatives of secondary classes and 2-normal bundles of foliations, J. Math. Sci. Univ. Tokyo, Vol.22 (2015), The special issue for the 20th anniversary, 893-937.
  18. Notes on `Infinitesimal derivative of the Bott class and the Schwarzian derivatives', Tohoku Math. J., Vol.69 (2017), 129-139.
  19. On Fatou and Julia sets of foliations, J. Math. Soc. Japan, Vol. 72 (2020), 1145-1159.
  20. On a characteristic class associated with deformations of foliations, preprint ('20/11/9), submitted. Also available at arXiv:2011.04340.

Monograph (October 20, 2021)

  1. Godbillon-Vey class of transversely holomorphic foliations, MSJ memoirs vol. 24, June 2010.

Survey articles (September 8, 2017)
* means the article is not refereed: it applies to 2, 6, 7, 8 and 9.

  1. Some results on secondary characteristic classes of transversely holomorphic foliations, in `Foliations: GEOMETRY AND DYNAMICS', pp. 3-16, World Scientific Publishing, Singapore, 2002.
  2. On existence and quasiconformal deformations of transversely holomorphic foliations* (PDF File, 64kbytes), Sūrikaisekikenkyūsho Kōkyūroku, Complex Dynamics, No. 1447 (2005), 15-19. This article is a survey for the paper 11 above, and is a note for the talk 6 below.
  3. On infinitesimal derivatives of the Bott class, in `Foliations 2005', pp. 37-46, World Scientific Publishing, Singapore, 2006. This is a survey for the paper 12 above, and is a note for the talks 7 and 8 below.
  4. On the Fatou-Julia decomposition of transversally holomorphic foliations of complex codimension one, Advanced Studies in Pure Mathematics, Vol.56 (2009), pp. 39-47, Mathematical Society of Japan. This is an announcement for the paper 13 above, and is based on the talks 11 and 12 below.
  5. On the Fatou-Julia decomposition of transversally holomorphic foliations of complex codimension one, in `Differential Geometry', Proceedings of the VIII International Colloquium Santiago de Compostela, Spain, 7-11 July 2008, World Scientific (2009), pp. 65-74. This is a brief survey for the paper 13 above, and is based on the talk 14 below. This article contains a few number of new results.
  6. On the Fatou-Julia decomposition of complex codimension-one transversely holomorphic foliations* (in Japanese, PDF File, 208kbytes), RIMS Kokyuroku No. 1661, Differential geometry of foliations and related topics on the Bergman kernel, July 2009, pp. 1-20. This is an article based on the talk in a conference held at RIMS, Kyoto in Dec. 2008.
  7. On Fatou-Julia decompositions of pseudosemigroups* (PDF File, 85kbytes), RIMS Kokyuroku No. 1699, Integrated Research on Complex Dynamics and its Related Fields, July 2010, 137-143. This is a survey for the paper 14 above, and based on a talk given at `2009 Complex Dynamics conference - Integrated Research on Complex Dynamics and its Related Fields -'.
  8. On Fatou-Julia decompositions of pseudosemigroups II* (PDF File, 101kbytes), RIMS Kokyuroku No. 1762, Research on Complex Dynamics and Related Fields, Nov. 2011, 125-133. This is a survey on the paper 14 above, and based on a talk given at `2010 Complex Dynamics conference - Integrated Research on Complex Dynamics and its Related Fields -'.
  9. Independence and non-triviality of rigid secondary complex characteristic classes* (PDF File, 87kbytes), RIMS Kokyuroku No. 1807, Integrated Research on Complex Dynamics, Sep. 2012, 74-79. This is a survey on the paper 15 above, and based on a talk given at `Complex Dynamics Conference of Academic Year 2011-2012 - Integrated Research on Complex Dynamics -'.
  10. On linear independence of classes in H*(WUq) (PDF File, 84kbytes), Jan. 2013. Accepted in the proceedings volume of GF2012 but not appeared by some reason (which I do not know). I have no plan to submit this article so that I will leave it here for the moment. This is a review on the paper 15, and is based on the talk 11 below.
  11. On deformations and rigidity of the Godbillon-Vey class, Geometry, Dynamics, and Foliations 2013, Advanced Studies in Pure Mathematics 72, 2017, 1-18.
  12. On the Fuks–Lodder–Kotschick class for deformations of foliations, Proceedings of the conference Contemporary Mathematics in Kielce 2020, February 24-27 2021, 2021, 1-15. This is a review on the paper 20, and is based on the talk 17 below.

Translations (September 8, 2017)

  1. On Thurston's construction of a surjective homomorphism H2n+1(BΓn,Z)→R, Tadayoshi Mizutani,Geometry, Dynamics, and Foliations 2013, Advanced Studies in Pure Mathematics 72, 2017, 211-219. Originally published in RIMS Kokyuroku No. 286 (the original article is written in Japanese). This article is refereed although it is a tranlation.

Thesis (appeared as research papers 5 and 6)


Talks at international conferences (July 14, 2021)

  1. The secondary characteristic classes of transversaly holomorphic foliations, at Complex Analysis in Dynamical Systems, IMPA-Rio de Janeiro, September 3, 1998.
  2. The Godbillon-Vey class of transversaly holomorphic foliations, at Foliations: Geometry and Dynamics, Banach Center (Warsaw), June 8, 2000.
  3. Residues of the Bott class, at New Directions in Dynamical Systems, Ryukoku University and Kyoto University, August 7, 2002.
  4. Residues of the Bott class, at Geometry and Foliations 2003 at Ryukoku University, 2003/9/11.
  5. Existence of transversely holomorphic structure of complex codimension one, at Topological and geometrical methods of complex differential equations, RIMS (Research Institute for Mathematical Sciences), Kyoto University, 2004/1/21.
  6. Infinitesimal derivative of the Bott class and the Schwarzian derivative, Foliations 2005, Wydział Matematyki Uniwersytetu Łódzkiego (Faculty of Mathematics of University of Lodz), Łódź (Lodz in Poland), 2005/6/14.
  7. On the Julia-Fatou decomposition of complex codimension-one folitaions, Niigata Workshop on Complex Geometry and Singularities, CrossPal Niigata, Niigata, 2007/8/24.
  8. A Fatou-Julia decomposition of complex codimension-one foliations, Global and Local Aspects of Holomorphic Foliations. In Honor of the 60th Birthday of Alcides Lins Neto, IMPA, Angra dos Reis, 2008/02/15.
  9. On the Fatou-Julia decomposition of transversally holomorphic foliations of complex codimension one, VIII International Colloquium on Differential Geometry, Santiago de Compostela (7-11 July, 2008), 2008/07/11.
  10. Infinitesimal deformations of foliations and Cartan connections, Geometry and Dynamics, Todai Forum 2011, UMPA ENS-Lyon, 2011/10/17.
  11. On independent rigid classes in H*(WUq), Foliations 2012, Wydział Matematyki i Informatyki, Uniwersytetu Łódzkiego (Faculty of Mathematics and Computer Science, University of Lodz), Łódź (Lodz in Poland), 2012/6/27.
  12. On Fatou-Julia decompositions of complex dynamical systems, Geometry and Foliations 2013, Graduate School of Mathematical Sciences, University of Tokyo, 2013/9/9. abstract
  13. Construction of secondary characteristic classes for foliations using the Chern-Weil theory, BGamma School, Faculty of Science and Engineering, Chuo University, 2013/9/18,19.
  14. Derivatives of the Godbillon-Vey class and transverse projective structures of foliations, 29th Summer Conference on TOPOLOGY and its APPLICATIONS (Sumtopo2014), College of Staten Island, 2014/7/23.
  15. A Chern-Weil construction for derivatives of characteristic classes, Foliations 2016, Będlewo (Poland), 2016/7/16.
  16. A remark on the Fatou sets of foliations of CP2, Complex foliations, dynamics and geometry, Universidade Federal Fluminense, Niterói, Rio de Janeiro (Brasil), 2018/7/24.
  17. On the Fuks-Lodder-Kotschick class for deformations of foliations, Contemporary Mathematics in Kielce 2020, Katedra Matematyki, Wydział Nauk Ścisłych i Przyrodniczych, Uniwersytetu Jana Kochanowskiego w Kielcach, Kielce (Poland), 2021/2/24 (planned in 2020 but held in 2021).

Talks at seminars abroad (September 8, 2017)

  1. Secondary characteristic classes of Transversely holomorphic foliations of complex codimension one, at Aarhus Universitet, March 13, 2000.
  2. Des dérivées infinitésimales de la classe de Bott et les dérivées schwarziennes, Le Séminaire de Mathématiques Pures, Unité de mathématiques pures et appliquées, École normale supérieur de Lyon, 2005/6/29.
  3. An introduction to secondary classes of foliations, Differential Geometry and Foliation Seminar, Centro de Investigacion en Matematicas (CIMAT), Guanajuato (Mexico), 2006/2/13.
  4. An introduction to secondary classes of foliations, Seminario de Sistemas Dinamicos y Ecuaciones Diferenciales, Instituto de Matemáticas, Unidad Morelia, Morelia (Mexico), 2006/2/20.
  5. Sur la décomposition Fatou-Julia de feuilletages transversalement holomorphes de complex codimension un, Analyse, géométrie et dynamique complexes, Laboratoire Emile Picard, Université Paul Sabatier, 2007/11/22.
  6. Sur la décomposition de Fatou-Julia d'un feuilletage transversalement holomorphes de codimension complex 1, Séminaire Géométrie - Topologie Dynamique, Département de Mathématiques de la Faculté des Sciences d'Orsay, 2009/03/18.
  7. Une construction de mesures δ-conformes pour des feuilletages transversalement holomorphes de codimension complexe 1, Dynamique et Géométrie complexes, Département de Mathématiques de la Faculté des Sciences d'Orsay, 2009/03/20.
  8. Autour de la décomposition de Fatou-Julia, Séminaire (Systèmes Dynamiques), Institut de Mathématiques de Toulouse, 2013/10/25.
  9. Autour de la décomposition de Fatou-Julia, Groupe de travaille ``Théorie ergodique et syetèmes dynamiques'', Département de Mathématiques d'Orsay (Paris), 2013/11/4.
  10. Autour de la décomposition de Fatou-Julia, Séminaires de Géométrie analytique, Institut de recherche mathématique de Rennes (Rennes), 2013/11/28.
  11. Quelques exemples de décomposition de Fatou-Julia pour des champs de vecteurs, Séminaire (Systèmes Dynamiques), Institut de Mathématiques de Toulouse (Toulouse), 2013/12/6.

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