■ 氏名
山口 俊博 (ヤマグチ トシヒロ)
YAMAGUCHI Toshihiro
■ 所属部局/職名
Research and Education Faculty, Natural Sciences Cluster, Science and Technology Unit/Professor
教育研究部 自然科学系 理工学部門/教授
■ 学部・学科・コース等
Faculty of Education, Teacher Training Division (Mathematics Education Course)
教育学部 学校教育教員養成課程(数学教育コース)
■ 連絡先
住 所
:
電 話
:
088-844-8383
F A X
:
E-Mail
:
tyamag●kochi-u.ac.jp
(送信の際は“●”を半角の“@”に変更して送信してください。)
U R L
:
http://www.cc.kochi-u.ac.jp/~tyamag
中村治名誉教授による掲載(情報数学関連)
■ 出身大学院・研究科等
岡山大学 博士(自然科学研究科 ) 1999 (修了)
■ 出身学校・専攻等
■ 取得学位
理学博士(1999.3) () 岡山大学
■ 研究職歴
■ 委員歴・役員歴
■ 受賞学術賞
■ 所属学会
■ 専門分野
代数的位相幾何学(代数的トポロジー、ホモトピー論)
■ 主な研究テーマ・活動
有理ホモトピー論ならではの切り口で、問題提議、解決したい。また、社会において本研究がどのような意味があるのか模索している。
■ 研究についてのPR
有理ホモトピー論は、有理数係数を使って位相不変量を考える「ゆるいトポロジー」で、有限の部分を考えない。その代わり、見通しがよく、速効性があり、幾何学の様々な分野に影響を与えている。
■ 社会人・生徒を対象として可能な講演・授業(例えば講演題目)
「トポロジーの発想」「グラフ理論入門」「やわらかい幾何学」「射影幾何入門」「トポロジーと囲碁」「幾何の補助教材としての4コマ漫画」
■ 研究業績(論文・解説)
Cartan calculi on the free loop spaces
arXiv:2207.05941 (Kuribayashi, Naito, Wakatsuki, Yamaguchi) /, 39 pages ()
A reduction of the string bracket to the loop product
arXiv:2109.1056 (Kuribayashi, Naito, Wakatsuki, Yamaguchi ) /, 30 pages ()
An example of non-coformal classifying space with rational H(2)-structure
MATHEMATICA (H.Nishinobu and T.Yamaguchi) /, 2022 (学術雑誌)
デザルグの目 -射影的分解の試み-
高知大学教育学部研究報告 (山口) 82/, 277-282 2022 (大学・研究所等紀要) http://hdl.handle.net/10126/00008530
Rational relative toral rank
Africa Mathematica (T.Yamaguchi) 33/2, 1-6 2022 (学術雑誌)
ホモトピー論における「三密」について
高知大学教育学部研究報告 (山口) 81/, 177-180 2021 (大学・研究所等紀要) http://hdl.handle.net/10126/00008049
Relative self-closeness numbers
Bull.Korean Math. Soc. (T.Yamaguchi) 58/2, 445-449 2021 (学術雑誌)
On ratios of homotopy and homology ranks of fibrations
Topology Proceedings (T.Yamaguchi and S.Yokura) 58/, 85-92 2021 (学術雑誌)
On a DGL-map between derivations of Sullivan minimal models
Arabian Journal of Math. (T.Yamaguchi) 9/, 739-754 2020 (学術雑誌)
Poincare polynomials of a map and a relative Hilali conjecture
Tbilisi Math. J. (T.Yamaguchi and S.Yokura) 13/4, 33-47 2020 (学術雑誌)
Self-closeness numbers of finite cell complexes
Topology and its Applications (N.Oda and T.Yamaguchi) 272/, 1-25 2020 (学術雑誌)
A proset structure induced from homotopy classes of maps and a classification of fibrations
Commun. Korean Math. Soc. (T.Yamaguchi and S.Yokura) 34/3, 991-1004 2019 (学術雑誌)
渋滞現象を記述する数理モデルを題材とした授業実践とその考察
高知大学教育学部研究報告 (加納、服部、中野、佐藤、山口、山中) /79, 65-70 2019 (大学・研究所等紀要) http://hdl.handle.net/10126/00007620
ICTを活用した図形探究活動についての一考察 -中学校第2学年「平行四辺形」単元における授業実践を通して-
高知大学 学校教育研究 (橋口、服部、中野、佐藤、山口、加納、袴田、岡本、楠瀬) 1/, 63-70 2019 (大学・研究所等紀要) http://hdl.handle.net/10126/00007657
Poset-stratified space structures of homotopy sets
Homology, Homotopy and Applications (T.Yamaguchi and S.Yokura) 21/2, 1-22 2019 (学術雑誌)
On a relative Hilali conjecture
African Diaspora J. of Math. (T.Yamaguchi and S.Yokura) 21/1, 81-86 2018 (学術雑誌)
Self-maps of spaces in fibrations
Homology, Homotopy and Applications (N.Oda and T.Yamaguchi) 20/2, 1-25 2018 (学術雑誌)
Self-homotopy equivalences and cofibrations
Topology and its Applications (N.Oda and T.Yamaguchi) 228/, 341-354 2017 (学術雑誌)
Certain maps preserving self-homotopy equivalences
J.Homotopy Relat. Struct. (Jin-Ho Lee and T.Yamaguchi) 12/3, 691-706 2017 (学術雑誌)
Rational cohomologies of classifying spaces for homogeneous spaces of small rank
Arabian Journal of Mathematics (H.Nishinobu and T.Yamaguchi) 5/, 225-237 2016 (学術雑誌)
Fiber-homotopy self-equivalences and a classification of fibrations in rational homotopy
J. Homotopy Relat. Struct. (T.Yamaguchi and S.Yokura) 11/, 957-972 2016 (学術雑誌)
Rational pairing rank of a map
African Diaspora Journal of Mathematics (T.Yamaguchi) 19/, 1-11 2016 (学術雑誌)
A fibre-restricted Gottlieb group and its rational realization problem
Topology and its Applications (T.Yamaguchi) 196/, 1060~1076 2015 (学術雑誌)
Sullivan minimal models of classifying spaces for non-formal spaces of small rank
Topology and its Appl. (H.Nishinobu and T.Yamaguchi) 196/, 290-307 2015 ()
Certain examples of posets of rational Gottlieb subgroups
Kochi J. Math. (H.Nishinobu and T.Yamaguchi) 10/, 77-94 2015 ()
The Lefschetz condition on projectivization of complex vector bundles
Communication Math. Korea (H.Nishinobu and T.Yamaguchi) 29/, 569-579 2014 ()
Pairing rank in rational homotopy group
African Diaspora J. of Math. (T.Yamaguchi) 17/, 85-92 2014 ()
Rational toral rank of a map
BULLETIN MATHEMATIQUE de Roumanie () 57/, 437-445 2014 ()
C-symplectic poset structure on a simply connected space
Topology and its Appl. (K.Hamada, T.Yamaguchi, S.Yokura) 161/, 107-126 2014 ()
Certain homotopy subgroups associated with a map
Kochi J.Math (T.Yamaguchi) 8/, 35-45 2013 ()
Pre-c-symplectic condition for the product of odd-spheres
J. Homotopy Relat. Struct. (J.Sato and T.Yamaguchi) 8/, 13-34 2013 ()
Examples of rational toral rank complex
I.J.M.M.S. (T.Yamaguchi) 2012/, ID 867247 2012 (学術雑誌)
有理トーラス階数4の基点付きグラフ
高知大学教育学部研究報告 (北村嘉久 山口) /72, 101-107 2012 (大学・研究所等紀要)
20次元以下のホモトピー階数型とコホモロジーシンプレクティック構造
高知大学教育学部研究報告 (中村治 山口) /72, 95-99 2012 ()
Examples of a Hasse diagram of free circle actions in rational homotopy
JP Journal of Geometry and Topology (T.Yamaguchi) 11/3, 181-191 2011 ()
A Hasse diagram for rational toral ranks
Bull.Belg.Math.Soc. (T.Yamaguchi) 18/, 493-508 2011 ()
Lower bounds of Betti numbers of elliptic spaces with certain formal dimensions.
Kochi Journal of Mathematics (O.Nakamura and T.Yamaguchi) 6/, 9-28 2011 (学術雑誌)
(n)-pairing with axes in rational homotopy.
Bull. Belg.Math. Soc. 17 (T.Yamaguchi,) /, 53-67 2010 (学術雑誌)
A rational obstruction to be a Gottlieb map.
J. Homotopy Relat.Struct. 5 (T.Yamaguchi) /, 97-111 2010 (学術雑誌)
Rational cohomologies of classifying spaces for homogeneous spaces of small rank
Arabian Journal of Mathematics (H.Nishinobu and T.Yamaguchi) 5/, 225-237 2016 (学術雑誌)
多角形の閉曲面へのグラフの埋め込み
高知大学教育学部研究報告 (後藤真孝、寒葉友樹、小野起奈、山口 ) /第69号, 135-138 2009 (大学・研究所等紀要)
An estimate in Gottlieb ranks of fibration
Bull. Belg. Math. Soc. 15 (T.Yamaguchi) /, 663-675 2008 (学術雑誌)
A lower bound for the rational LS-category of a coformal elliptic space.
Math. J. Okayama Univ. 50 (T.Yamaguchi,) /, 201--203 2008 ()
多角形の擬曲面の分類
高知大学教育学部研究報告 (井上朋久、宮本智之、山口 ) /第68号, 159-164 2008 (大学・研究所等紀要)
CUP_0 and CAT_0 can be arbitrary in elliptic spaces.
New Zealand J. Math. 35, no. 2 (T,Yamaguchi) /, 211--213 2006 ()
A rational splitting of a based mapping space.
Algebr. Geom. Topol. 6 (Kuribayashi, Katsuhiko; Yamaguchi, Toshihiro) /, 309--327 2006 ()
On a lower bound for the L-S category of a rationally elliptic space.
Bull. Belg. Math. Soc. Simon Stevin 12, no. 4 (Yamaguchi, Toshihiro ) /, 565--568. 2005 (学術雑誌)
A lower bound for the LS category of a formal elliptic space.
Math. J. Okayama Univ. 47 (Kotani, Yasusuke; Yamaguchi, Toshihiro ) /, 141--145 2005 ()
An example of a fiber in fibrations whose Serre spectral sequences collapse.
Czechoslovak Math. J. 55(130) , no. 4, (Yamaguchi, Toshihiro ) /, 997--1001 2005 ()
When is the classifying space for elliptic fibrations rank one?
Bull. Korean Math. Soc. 42, no. 3 (Yamaguchi, Toshihiro ) /, 521--525 2005 ()
Rational toral ranks in certain algebras.
Int. J. Math. Math. Sci. no. 69-72, (Kotani, Yasusuke; Yamaguchi,Toshihiro ) /, 3765--3774 2004 ()
On the genus of free loop fibrations over $F\sb 0$-spaces.
Int. J. Math. Math. Sci. no. 65-68 (Yamaguchi, Toshihiro) /, 3617--3619 2004 ()
Rationally elliptic spaces with isomorphic cohomology algebras.
J. Pure Appl. Algebra 187 no. 1-3, (Nishimoto, Tetsu; Shiga, Hiroo; Yamaguchi,) /, 241--254 2004 ()
The set of rational homotopy types with given cohomology algebra.
Homology Homotopy Appl. 5 (2003), no. 1 (Shiga, Hiroo; Yamaguchi, Toshihiro ) /, 423--436 ()
A comment on toral rank for a conjecture of Halperin.
JP J. Geom. Topol. 3, no. 3 (Yamaguchi, Toshihiro) /, 221--224 2003 ()
Elliptic rational spaces whose cohomologies and homotopies are isomorphic.
Topology 42 ,no. 6 (Nishimoto, Tetsu; Shiga, Hiroo; Yamaguchi, Toshihiro ) /, 1397--1401 ()
Principal bundle maps via rational homotopy theory.
Publ. Res. Inst. Math. Sci. 39, no. 1 (Shiga, Hiroo; Yamaguchi, Toshihiro ) /, 49--57 2003 ()
The cohomology of classifying space of fibrations with elliptic fiber is infinite dimensional.
Ryukyu Math. J. 14 (Yamaguchi, Toshihiro ) /, 119--121 2001 ()
Principal $S\sp 1$-bundles and forgetful maps.
Groups of homotopy self-equivalences and related topics(Gargnano, 1999), 293--297, Contemp. Math., 274, Amer. Math. Soc., Providence, RI, 2001 (Shiga, H.; Tsukiyama, K.; Yamaguchi, T. ) /, ()
On additive $K$-theory with the Loday-Quillen ${}\sp *$-product.
Math. Scand. 87, no. 1, 5--21. (Kuribayashi, Katsuhiko; Yamaguchi, Toshihiro ) /, 2000 ()
Formality of the function space of free maps into an elliptic space.
Bull. Soc. Math. France 128 (2000), no. 2 (Yamaguchi, Toshihiro ) /, 207--218 ()
Examples of elliptic models which are oddly generated and don
Ryukyu Math. J. 12 () /, 87--92 ()
The vanishing problem of the string class with degree $3$.
J. Austral. Math. Soc. Ser. A 65, no.1 (Kuribayashi, Katsuhiko; Yamaguchi, Toshihiro) /, 129--142. 1998 ()
On characterizations of rational homotopy types with some rational cyclic cohomologies.
Stable and unstable homotopy (Toronto, ON, 1996), 299--312, Fields Inst. Commun., 19, Amer. Math. Soc., Providence, RI, 1998. (Yamaguchi, Toshihiro ) /, ()
The cohomology algebra of certain free loop spaces.
Fund. Math. 154 (1997), no. 1 (Kuribayashi, Katsuhiko; Yamaguchi, Toshihiro ) /, 57--73 ()
■ 研究業績(著書)
■ 研究業績(口頭・ポスター)
■ 研究業績(特許)
■ 研究業績(その他の活動)
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