| 1. |
蔦谷充伸, Higher homotopy normalities in topological groups, ホモトピー論シンポジウム, 2023.11. |
| 2. |
＠Mitsunobu Tsutaya, Homotopy types of spaces of finite propagation unitary operators on Z, CREST Research Seminar on "Theoretical studies of topological phases of matter", 2023.10. |
| 3. |
蔦谷充伸, Higher homotopy normalities in topological groups, トポロジーシンポジウム, 2023.08, 正規部分群による商が群になることの一般化として, Farjoun-Segev は topological crossed module のホモトピー商が自然に位相群になることを示した. 本講演では高次ホモトピーを用いた crossed module の一般化である Nk(l)-map (k, l ≥ 1) を導入する. これは McCarty や James により定義された古典的なホモトピー正規性よりも強い性質となっている. Nk(l)-map はファイバーワイズ射影空間を用いたよい特徴付けを持つ. また, Nk(l)-map のホモトピー商は LS カテゴリーが小さいとき, H-空間となることを示す. さらに応用として, 包含写像 SU(m) → SU(n) がいつ p-局所的に Nk(l)-map となるのか調べる.. |
| 4. |
Mitsunobu Tsutaya, An associative model of homotopy coherent functors and natural transforamations, 関西代数トポロジーセミナー, 2023.02. |
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Mitsunobu Tsutaya, Finite propagation operators and Hilbert bundles with end, Topology Seminar, 2022.09. |
| 6. |
Mitsunobu Tsutaya, Higher homotopy normalities in topological groups, Classifying spaces in homotopy theory: in honour of Ran Levi's 60th Birthday, 2022.09. |
| 7. |
蔦谷充伸, Homotopy normalities in topological groups, 京都・九州・信州トポロジーセミナー, 2021.12, 正規部分群はcrossed moduleと呼ばれる対象に一般化される．crossed moduleは準同型 H -> G とそれと整合的な「共役作用」 G -> Aut(H) からなるようなものである．正規部分群による商が群になることの一般化として，Farjoun-Segevはtopological crossed moduleのホモトピー商が自然に位相群になることを示した．本講演では高次ホモトピーを用いたcrossed moduleの一般化であるN_k(l)-map (k,l ≥ 1)を導入する．これはMcCartyやJamesにより定義された古典的なホモトピー正規性よりも強い性質となっている．N_k(l)-mapはファイバーワイズ射影空間を用いた特徴付けを持つ．また，N_k(l)-mapはそのホモトピー商のLSカテゴリーが小さいとき，H-空間となることを示す．さらに応用として，包含写像 SU(m) -> SU(n) がいつp-局所的にN_k(l)-mapとなるのか調べる．. |
| 8. |
蔦谷充伸, Finite propagation operators and Hilbert bundles with end, 東京都立大学・ハイブリッド幾何学セミナー, 2021.06. |
| 9. |
Mitsunobu Tsutaya, Homotopy type of the space of finite propagation unitary operators on Z, Southampton-Kyoto Workshop II, 2020.12, The index theory for the space of finite propagation unitary operators was developed by Gross, Nesme, Vogts and Werner from the viewpoint of quantum walks in
mathematical physics. In particular, they proved that π0 of the space is determined by the index. However, nothing is known about the higher homotopy groups. In this talk,
we describe the homotopy type of the space of finite propagation unitary operators on the Hilbert space of square summable C-valued Z-sequences, so we can determine its homotopy
groups.. |
| 10. |
Mitsunobu Tsutaya, Homotopy types of spaces of finite propagation unitary operators on Z, WORKSHOP: unitary operators: spectral and topological properties, 2020.09. |
| 11. |
蔦谷充伸, Unstable homotopy types of spaces of finite propagation unitary operators on Z, 関西ゲージ理論セミナー、京都代数トポロジーセミナー合同セミナー, 2020.09. |
| 12. |
Mitsunobu Tsutaya, Characterizations of homotopy fiber inclusion, Homotopy Theory Symposium, 2019.11, It is well-known that a homotopy fiber sequence generated by a map G --> X extends twice to the right if and only if G admits a structure of a topological group and the map extends to an action of G on X up to homotopy equivalence. Similarly, a homotopy fiber sequence generated by a map H --> G extends three times to the right if and only if H and G admit structures of topological groups and the map is a homomorphism up to homotopy equivalence. But characterizations of "homotopy fiber inclusions" do not seem to be studied in detail. In this talk, we show some characterizations of homotopy fiber inclusions and some examples.. |
| 13. |
蔦谷充伸, De Rham cohomology of the weak stable foliation of the geodesic flow of a hyperbolic surface, リーマン面に関連する位相幾何学, 2019.09, Let S be a closed hyperbolic surface. Then the geodesic flow on the unit tangent bundle M of S is an Anosov flow. It defines a 2-dimensional foliation F on M. We determine the leafwise cohomologies of F with respect to various coefficients. Our method is rather representation theoretic. As applications, we study the deformation of F and the parameter deformation of the canonical locally free action of the affine transformation group on M.. |
| 14. |
蔦谷充伸, Homotopy thoery of An-spaces in Lie groups, 京都大学理学研究科数学教室談話会, 2019.06. |
| 15. |
蔦谷充伸, On the cohomology of the orbit foliation of certain group action on the unit circle bundle of a closed hyperbolic surface, 信州トポロジーセミナー, 2018.12. |
| 16. |
Mitsunobu Tsutaya, Pontryagin–Thom construction in topological coincidence theory, ホモトピー沖縄, 2018.09. |
| 17. |
Mitsunobu Tsutaya, An-maps and mapping spaces, Mapping Spaces in Algebraic Topology, 2018.08, An-maps are morphisms between An-spaces introduced by Sugawara, Stasheff, Boardman-Vogt and Iwase. Sugawara, Stasheff and Iwase characterised the condition when a map between An-spaces admits an An-map structure in terms of projective spaces. In this talk, we see that a refinement of this result is realised as a weak homotopy equivalence between the space of An-maps An(G,H) and the space of based maps Map∗(BnG,BH) from the n-th projective space BnG to the classifying space BH. We also see some applications of this results to extension of an evaluation fibration and homotopy commutativity.. |
| 18. |
Mitsunobu Tsutaya, Mapping spaces from projective spaces, International Conference on Manifolds, Groups and Homotopy, 2018.06. |
| 19. |
蔦谷充伸, Tfn-property of BSU(2) and relation to fiberwise An-triviality, 福岡ホモトピー論セミナー, 2018.01. |
| 20. |
蔦谷充伸, Higher homotopy commutativity in localized Lie groups and gauge groups, ホモトピー論シンポジウム, 2017.11. |
| 21. |
Mitsunobu Tsutaya, Homotopy theoretic classifications of gauge groups, Young Researchers in Homotopy Theory and Toric Topology 2017, 2017.08. |
| 22. |
蔦谷充伸, Applications of Stasheff's A∞-theory to Lie groups, 日本数学会2017年度年会, 2017.03. |
| 23. |
Mitsunobu Tsutaya, Infiniteness of A∞-types of gauge groups, Friday's Topology Seminar, 2017.02. |
| 24. |
Mitsunobu Tsutaya, Higher homotopy commutativity in localized Lie groups and gauge groups, Topology & Malaga Meeting, 2017.02. |
| 25. |
蔦谷充伸, Stasheff's An-structure and related topics, 京大代数トポロジーセミナー, 2016.12. |
| 26. |
蔦谷充伸, Coincidence Reidemeister trace and its generalization, Group Action and Topology, 2016.12. |
| 27. |
蔦谷充伸, Coincidence Reidemeister trace and its generalization, ホモトピー論シンポジウム, 2016.11. |
| 28. |
蔦谷充伸, Finiteness of An-equivalence types of gauge groups, 日本数学会2016年度秋季総合分科会, 2016.09. |
| 29. |
蔦谷充伸, Reidemeister trace and its generalization, 京大代数トポロジーセミナー, 2016.09. |
| 30. |
蔦谷充伸, On the homotopy types of the spaces of maps to classifying spaces, Matsuyama Seminar on Topology, Geometry, Set theory and their Applications, 2016.07. |
| 31. |
蔦谷充伸, Homotopy theoretic classification of gauge groups, 福岡大学トポロジーセミナー, 2016.05. |
| 32. |
蔦谷 充伸, Mapping spaces from projective spaces, トポロジー金曜セミナー, 2016.04, 位相群のA_n-構造（n=1,2,...,∞）は位相群の演算に関する高次ホモトピー構造を記述するもので、射影空間の一般化や、LSカテゴリーなどの不変量と関係がある。位相群の間のA_n-構造を保つ写像（A_n-写像）は、基点を保つ写像より強く、準同型写像よりも弱い、自然な概念である。しかし定義に高次ホモトピーが現れるため、障害理論などの取扱いが一般には困難である。本講演では、射影空間からの写像のなす空間を用いてA_n-写像のなす空間のホモトピー型を記述する講演者の結果を与え、その応用を紹介する。. |
