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 Topology Seminar at Kyushu University (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. arXiv:1612.08816 (with S. Hasui and D. Kishimoto)
    Higher homotopy commutativity in localized Lie groups and gauge groups,
  2. arXiv:1606.07363
    Coincidence Reidemeister trace and its generalization,
  3. MR3679077 (with D. Kishimoto and S. Theriault)
    The homotopy types of G2 gauge groups
    Topology Appl. 228 (2017), 92-107.
  4. arXiv:1405.0337 (with D. Kishimoto)
    Samelson products in p-regular SO(2n) and its homotopy normality,
    accepted for publication by Glasg. Math. J.
  5. MR3491849 arXiv:1408.2010
    Mapping spaces from projective spaces,
    Homology, Homotopy Appl. 18 (2016), 173-203.
  6. MR3465846 arXiv:1502.02781 (with D. Kishimoto)
    Infiniteness of A-types of gauge groups,
    J. Topol. 9 (2016), 181-191.
  7. MR3327166 arXiv:1210.8252
    Homotopy pullback of An-spaces and its applications to An-types of gauge groups,
    Topology Appl. 187 (2015), 1-25.
  8. 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.
  9. 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.
  10. MR3071142 (with D. Kishimoto and A. Kono)
    Mod p decompositions of gauge groups
    Algebr. Geom. Topol. 13 (2013), 1757-1778.
  11. MR2876314 arXiv:1107.3908
    Finiteness of An-equivalence types of gauge groups,
    J. London Math. Soc. 85 (2012), 142-164.
  12. 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. Homotopy theoretic classification of gauge groups,
    lecture notes based on the series talk in Fukuoka University 2016, in preparation.
  2. Evaluation fiber sequence and homotopy commutativity,
    lecture notes for Algebraic Topology Workshop for Young Researches 2015.

Other Documents

  1. M. Tsutaya,
    On evaluation fiber sequences,
    RIMS Kokyuroku No. 1922, The Topology and the Algebraic Structures of Transformation Groups, 166-169.
  2. 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),
  3. 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 2017-

  1. Notes
    Homotopy theoretic classifications of gauge groups,
    Young Researchers in Homotopy Theory and Toric Topology 2017, Kyoto University, August 2017.
  2. Slides
    Applications of Stasheff's A-theory to Lie groups,
    MSJ Spring Meeting 2017, Tokyo Metropolitan University, March 2017.
  3. Infiniteness of A-types of gauge groups,
    Friday's Topology Seminar, Autonomous University of Barcelona, February 2017.
  4. Notes
    Higher homotopy commutativity in localized Lie groups and gauge groups,
    Topology & Malaga Meeting, University of Malaga, Februrary 2017.

Talks 2014-2016

Homotopy Seminar

Curriculum Vitae


- 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


- D.S., Kyoto University, November 2011

- M.S., Kyoto University, March 2010


- 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


- 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