Mitsunobu TSUTAYA

Faculty of Mathematics, Kyushu University, Fukuoka, 819-0395, Japan.

tsutaya_at_math_dot_kyushu-u.ac_dot_jp (please replace "_at_" by "@" and "_dot_" by ".")

I am the organizer of the Kyushu University Topology Seminar (Fridays 16:00-17:00).

講義関連 (Japanese)

Research Interest

algebraic topology, An-spaces, operads, mapping spaces, homotopy theory of Lie groups


  1. (with N. Iwase)
    Upper bound for monoidal topological complexity,
    accepted for publication in Kyushu J. Math.
  2. arXiv:1606.07363
    Coincidence Reidemeister trace and its generalization,

Published Papers

  1. MR3975098 arXiv:1807.02944 (with N. Iwase and M. Sakai)
    A short proof for tc(K)=4,
    Topology Appl. 264 (2019), 167-174.
  2. MR3852292 arXiv:1612.08816 (with S. Hasui and D. Kishimoto)
    Higher homotopy commutativity in localized Lie groups and gauge groups,
    Homology, Homotopy Appl. 21 (2019), 107-128.
  3. MR3811091
    Corrigendum to `Homotopy pullback of An-spaces and its applications to An-types of gauge groups' [Topology Appl. 187 (2015) 1–25],
    Topology Appl. 243 (2018), 159-162.
  4. MR3733837 arXiv:1405.0337 (with D. Kishimoto)
    Samelson products in p-regular SO(2n) and its homotopy normality,
    Glasg. Math. J. 60 (2018), 165-174.
  5. MR3679077 (with D. Kishimoto and S. Theriault)
    The homotopy types of G2 gauge groups
    Topology Appl. 228 (2017), 92-107.
  6. MR3491849 arXiv:1408.2010
    Mapping spaces from projective spaces,
    Homology, Homotopy Appl. 18 (2016), 173-203.
  7. MR3465846 arXiv:1502.02781 (with D. Kishimoto)
    Infiniteness of A-types of gauge groups,
    J. Topol. 9 (2016), 181-191.
  8. MR3327166 arXiv:1210.8252 !!Erratum!!
    Homotopy pullback of An-spaces and its applications to An-types of gauge groups,
    Topology Appl. 187 (2015), 1-25.
  9. MR3194181 (with D. Kishimoto and A. Kono)
    On localized unstable K1-groups and applications to self-homotopy groups,
    Canad. Math. Bull. 57 (2014), 344-356.
  10. MR3164541 (with D. Kishimoto and A. Kono)
    On p-local homotopy types of gauge groups,
    Proc. Roy. Soc. Edinburgh: Sect. A 144 (2014), 149-160.
  11. MR3071142 (with D. Kishimoto and A. Kono)
    Mod p decompositions of gauge groups
    Algebr. Geom. Topol. 13 (2013), 1757-1778.
  12. MR2876314 arXiv:1107.3908
    Finiteness of An-equivalence types of gauge groups,
    J. London Math. Soc. 85 (2012), 142-164.
  13. MR2864856 arXiv:1101.4278
    A note on homotopy types of connected components of Map(S4,BSU(2)),
    J. Pure and Appl. Algebra 216 (2012), 826-832.

Lecture Notes

  1. 蔦谷充伸,
    幾何学的バー構成の基本性質と応用 (Japanese),
  2. Evaluation fiber sequence and homotopy commutativity,
    lecture notes for Algebraic Topology Workshop for Young Researches 2015.

Other Documents

  1. M. Tsutaya,
    Results in Homotopy Theory of Gauge Groups.
  2. M. Tsutaya,
    On evaluation fiber sequences,
    RIMS Kokyuroku No. 1922, The Topology and the Algebraic Structures of Transformation Groups, 166-169.
  3. 井澤昇平・大下達也・蔦谷充伸・野坂武史,
    代数的K-理論の基礎とその周辺 (Japanese),
  4. 伊藤哲也・今城洋亮・蔦谷充伸・野坂武史,
    Atiyah-Singer の指数定理 (Japanese),

Talks 2018-

  1. Characterizations of homotopy fiber inclusion,
    Homotopy Theory Symposium, Hokkaido University, October 2019.
  2. Reidemeister trace and Pontryagin-Thom construction,
    Reidemeister traces and gauge theory, the University of Ryukyus, October 2019.
  3. Slides
    De Rham cohomology of the weak stable foliation of the geodesic flow of a hyperbolic surface,
    Topological Studies around Riemann Surfaces, the University of Tokyo, September 2019.
  4. Slides
    Homotopy thoery of An-spaces in Lie groups,
    Colloquium, Kyoto University, June 2019.
  5. On the cohomology of the orbit foliation of certain group action on the unit circle bundle of a closed hyperbolic surface,
    Shinshu Topology Seminar, Shinshu University, December 2018.
  6. Slides
    Pontryagin–Thom construction in topological coincidence theory,
    Homotopy Okinawa, Okinawaken Seinenkaikan, September 2018.
  7. Slides
    An-maps and mapping spaces,
    Mapping Spaces in Algebraic Topology, Kyoto University, August 2018.
  8. Slides
    Mapping spaces from projective spaces,
    International Conference on Manifolds, Groups and Homotopy, Sabhal Mòr Ostaig, June 2018.
  9. Notes
    Tfn-property of BSU(2) and relation to fiberwise An-triviality,
    Homotopy Theory Seminar 2018, Fukuoka University, January 2018.

Talks 2014-2017

Homotopy Seminar

Curriculum Vitae

Profesional experience

- Assistant Professor, Kyushu Uniersity, May 2016 - present

- JSPS Research Fellow PD, Kyushu University, April 2016

- Research Associate, Kyoto University, April 2013 - May 2016

- JSPS Research Fellow PD, Kyoto University, December 2011 - March 2013

- JSPS Research Fellow DC1, Kyoto University, April 2010 - November 2011

Seminars and conferences

- Kyushu University Topology Seminar - organizer, April 2017 - present


- D.S., Kyoto University, November 2011

- M.S., Kyoto University, March 2010


- Grant-in-Aid for Early-Career Scientists, Japan Society for the Promotion of Science, April 2019 - March 2022

- Grant-in-Aid for Young Scientists (B), Japan Society for the Promotion of Science, April 2016 - March 2019

- Grant for Basic Science Research Projects, Sumitomo Foundation, November 2015 - November 2016

- Grant-in-Aid for JSPS Fellows, Japan Society for the Promotion of Science, April 2010 - March 2013

Teaching experience

- Calculus II, Second Semester 2019

- Geometry I Exercise (manifolds), First Semester 2019

- Calculus III, First Semester 2019 (2 classes)

- Geometry II Exercise (homology of topological spaces), Second Semester 2018

- Calculus II, Second Semester 2018

- Geometry I Exercise (manifolds), First Semester 2018

- Calculus I, First Semester 2018

- Geometry II Exercise (homology of topological spaces), Second Semester 2017

- Geometry I Exercise (manifolds), First Semester 2017

- Survey in Mathematics II Exercise (metric spaces), First Semester 2017

- Linear Algebra, First Semester 2017

- Survey in Mathematics III Exercise (general topology), Second Semester 2016

- Survey in Mathematics I Exercise (convergence of series and sequence of functions), First Semester 2016