Mitsunobu TSUTAYA

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

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

学生向け情報 (講義，集中講義，数学の話題，大学院進学について)

Research Interest

algebraic topology, A_n-spaces, higher homotopy, mapping spaces, homotopy theory of Lie groups

Preprints

arXiv:2404.01510 (with S. Hasui, D. Kishimoto and Y. Tong)
Homotopy commutativity in quasitoric manifolds,
preprint.
arXiv:2302.01017 (with D. Kishimoto and M. Takeda)
The space of commuting elements in a Lie group and maps between classifying spaces,
accepted for publication in Proc. Roy. Soc. Edinburgh: Sect. A.
arXiv:2211.00512 (with T. Kato and D. Kishimoto)
Vector fields on non-compact manifolds,
accepted for publication in Algebr. Geom. Topol.
arXiv:2105.02981 (with T. Kato and D. Kishimoto)
Hilbert bundles with ends,
accepted for publication in J. Topol. Anal.

Published Papers

arXiv:2101.10596 (with S. Hasui, D. Kishimoto and M. Takeda)
Tverberg's theorem for cell complexes,
Bull. Lond. Math. Soc. 55 (2023), 1551-2086.
arXiv:2102.00606 (with T. Kato and D. Kishimoto)
Homotopy type of the unitary group of the uniform Roe algebra on Zⁿ,
J. Topol. Anal. 15 (2023), 495-512.
arXiv:2007.06787 (with T. Kato and D. Kishimoto)
Homotopy type of the space of finite propagation unitary operators on Z,
Homology, Homotopy Appl. 25 (2023), 375-400.
arXiv:2111.15096
Higher homotopy normalities in topological groups,
J. Topol. 16 (2023), 234-263.
arXiv:2012.15372 MR4527556 (with M. Tsukamoto and M. Yoshinaga)
G-index, topological dynamics and marker property,
Israel J. Math. 251 (2022), 737-764.
MR4129805 (with N. Iwase)
Upper bound for monoidal topological complexity,
Kyushu J. Math. 74 (2020), 197-200.
arXiv:1807.02944 MR3975098 (with N. Iwase and M. Sakai)
A short proof for tc(K)=4,
Topology Appl. 264 (2019), 167-174.
arXiv:1612.08816 MR3852292 (with S. Hasui and D. Kishimoto)
Higher homotopy commutativity in localized Lie groups and gauge groups,
Homology, Homotopy Appl. 21 (2019), 107-128.
MR3811091
Corrigendum to `Homotopy pullback of A_n-spaces and its applications to A_n-types of gauge groups' [Topology Appl. 187 (2015) 1–25],
Topology Appl. 243 (2018), 159-162.
arXiv:1405.0337 MR3733837 (with D. Kishimoto)
Samelson products in p-regular SO(2n) and its homotopy normality,
Glasg. Math. J. 60 (2018), 165-174.
MR3679077 (with D. Kishimoto and S. Theriault)
The homotopy types of G₂ gauge groups,
Topology Appl. 228 (2017), 92-107.
arXiv:1408.2010 MR3491849
Mapping spaces from projective spaces,
Homology, Homotopy Appl. 18 (2016), 173-203.
MR3465846 arXiv:1502.02781 (with D. Kishimoto)
Infiniteness of A_∞-types of gauge groups,
J. Topol. 9 (2016), 181-191.
arXiv:1210.8252 MR3327166 !!Erratum!!
Homotopy pullback of A_n-spaces and its applications to A_n-types of gauge groups,
Topology Appl. 187 (2015), 1-25.
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.
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.
MR3071142 (with D. Kishimoto and A. Kono)
Mod p decompositions of gauge groups,
Algebr. Geom. Topol. 13 (2013), 1757-1778.
arXiv:1107.3908 MR2876314
Finiteness of A_n-equivalence types of gauge groups,
J. London Math. Soc. 85 (2012), 142-164.
arXiv:1101.4278 MR2864856
A note on homotopy types of connected components of Map(S⁴,BSU(2)),
J. Pure and Appl. Algebra 216 (2012), 826-832.

Unpublished papers

arXiv:2103.12403 (with H. Maruhashi)
De Rham cohomology of the weak stable foliation of the geodesic flow of a hyperbolic surface,
preprint.
arXiv:1606.07363
Coincidence Reidemeister trace and its generalization,
preprint.

Lecture Notes

Evaluation fiber sequence and homotopy commutativity,
lecture notes for Algebraic Topology Workshop for Young Researches 2015.

Other Documents

M. Tsutaya,
Results in Homotopy Theory of Gauge Groups (last update: Feb. 13, 2022).
M. Tsutaya,
On evaluation fiber sequences,
RIMS Kokyuroku No. 1922, The Topology and the Algebraic Structures of Transformation Groups, 166-169.
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)，
第六回琵琶湖若手数学者勉強会（2012年2月）報告書
伊藤哲也・今城洋亮・蔦谷充伸・野坂武史，
Atiyah-Singer の指数定理 (Japanese)，
第五回琵琶湖若手数学者勉強会（2011年2月）報告書

Talks 2019-

Higher homotopy normalities in topological groups,
Homotopy Theory Symposium, Osaka Metropolitan University, November 2023.
Homotopy types of spaces of finite propagation unitary operators on Z,
CREST Research Seminar on "Theoretical studies of topological phases of matter", online, October 2023.
Slides
Higher homotopy normalities in topological groups,
Topology Symposium, Nara Women's University, August 2023.
Slides
An associative model of homotopy coherent functors and natural transforamations,
Kansai Algebraic Topology Seminar, Osaka Metropolitan University, February 2023.
Finite propagation operators and Hilbert bundles with end,
Topology Seminar, the University of Aberdeen, September 2022.
Slides
Higher homotopy normalities in topological groups,
Classifying spaces in homotopy theory: in honour of Ran Levi's 60th Birthday, ICMS, Bayes Centre, the University of Edinburgh, September 2022.
Slides
Homotopy normalities in topological groups,
Kyoto-Kyushu-Shinshu Topology Joint Seminar, online, December 2021.
Slides
Finite propagation operators and Hilbert bundles with end,
TMU Geometry Seminar, online, Tokyo Metropolitan University, June 2021.
Slides
Homotopy type of the space of finite propagation unitary operators on Z,
Southampton-Kyoto Workshop II, online, December 2020.
Slides
Homotopy types of spaces of finite propagation unitary operators on Z,
WORKSHOP: unitary operators: spectral and topological properties, online, September 2020.
Slides
Unstable homotopy types of spaces of finite propagation unitary operators on Z,
joint seminar of Kansai gauge theory seminar and Kyoto algebraic topology seminar, online seminar, May 2020.
Characterizations of homotopy fiber inclusion,
Homotopy Theory Symposium, Hokkaido University, October 2019.
Reidemeister trace and Pontryagin-Thom construction,
Reidemeister traces and gauge theory, the University of Ryukyus, October 2019.
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.
Slides
Homotopy theory of A_n-spaces in Lie groups,
Colloquium, Kyoto University, June 2019.