2001 Fiscal Year Annual Research Report

高次元多面体とoperadの研究

Research Project

Project/Area Number	13640080
Research Institution	Kochi University
Principal Investigator	逸見豊高知大学, 理学部, 教授 (70181477)
Co-Investigator(Kenkyū-buntansha)	森杉馨和歌山大学, 教育学部, 教授 (00031807) 小松和志高知大学, 理学部, 助教授 (00253336) 下村克己高知大学, 理学部, 教授 (30206247) 河本裕介防衛大学校, 綜合教育学群, 助手築山耕三島根大学, 教育学部, 教授 (20093651)
Keywords	ポップ空間 / quasi p-regular / unstable higher order operation / 高位ヒモトピー可換性 / 準Cp-空間 / mod p torus theorem / 球面のホモトピー群 / タイリング空間
Research Abstract	研究実施計画の役割分担に従って,下記の研究成果を得た. 1.mod p有限H-spaceがquasi p-regularになるための条件を調べ,Kumpelのp-regulraityに関する結果の一般化を示した.これはHarper, McClearly, Wilkersonらの結果を含むものである. 2.奇素数pに対して,unstable p-th order mod p cohomology operationを定義し,それを用いて,ある種のcohomologyを持つH-spaceは存在しないことを示した. 3.Williamsによって与えられた結合的H-spaceの積の高位ホモトピー可換性の定義を高位ホモトピー結合的H-spaceに対して拡張した.さらにそれを用いて,有限生成コホモロジー環を持つH-spaceに関するmod p torus定理を与えた. 4.下村克己は,υ^<-1>_2BPで局所化された球面のホモトピー群に収束するAdams-Novikovスペクトル系列のE_<2->項を素数2で決定した。 5.小松和志はroot latticesから射影法により得られるタイリング空間の周期とその最大数を特徴付けた.またintegral latticesの場合にも同様の結果の成立を示した. 6.森杉馨はHopf map η_2:S^3→S2の懸垂η_n∈π_<n+1>(S^n)のMoore space M^n=S^<n-1>∪e^nへのlift <η_n>^^^^∈π_<n+1>(M^n)のWhitehead積[<η_n>^^^^,<η_n>^^^^]について調べた。また球面の非安定homotopy群の元が,いつmod 2 Moore spaceに1iftするかについて調べた. 7.河本裕介は単連結な準C_<ρ->空間でそのmod pコホモロジー環が有限生成環であるものは,CP^∞有限個の直積にホモトピー同値であることを示した.

Research Products

(17 results)

All Other

All Publications (17 results)

[Publications] Y.Hemmi: "Mod p decompositions of mod p finite H-spaces"Mem. Fac. Sci. Kochi Univ. Ser. A (Math.). 22. 59-65 (2001)
[Publications] Y.Hemmi, J.Lin: "Cohomology Rings of 3-local Finite H-spaces"J. Pure Appl. Algebra. (印刷中).
[Publications] Y.Hemmi: "Unstable p-th order operation and H-spaces"Contemporary Math.. (印刷中).
[Publications] Y.Kamiya, K.Shimomura: "The homotopy groups π_*(L_2V(0)∧T(k))"Hiroshima Math. J.. 31. 391-408 (2001)
[Publications] K.Shimomura, X.Wang: "The homotopy groups π_*(L_2S^0) at the prime 3"Topology. (印刷中).
[Publications] K.Shimomura: "The homotopy groups π_*(L_nT(m)∧V(n-2))"Contemporary Math.. (印刷中).
[Publications] K.Shimomura, X.Wang: "The Adams-Novikov E_2-term for π_*(L_2S^0) at the prime 2"Math. Z.. (印刷中).
[Publications] Y.Kamiya, K.Shimomura: "E_*-homology spheres for a connective spectrum E"Contemporary Math.. (印刷中).
[Publications] T.Kobayashi, K.Komatsu: "Extendibility and stable extendibility of vector bundles over real projective spaces"Hiroshima Math. J.. 31. 99-106 (2001)
[Publications] K.Komatsu: "Periods of cut-and-project tiling spaces from root lattices"Hiroshima Math. J.. 31. 435-438 (2001)
[Publications] S.Ishiguro, K.Komatsu: "Symmetries of cut-and-project tilings corresponding to exceptional folding"Mem. Fac. Sci. Koch Univ. (Math.). 22(印刷中). (2001)
[Publications] T.Kobayashi, K.Komatsu: "Extendibility and stable extendibility of the square of the normal bundle associated to an immersion of the real projective space"Hiroshima Math. J.. (印刷中).
[Publications] K.Morisugi: "Composition sturctnre of the self maps of SU(3) and Sp(2)"Contemporary Math.. 274. 233-240 (2001)
[Publications] K.Morisugi: "The Whitehead square of a lift of the Hopf map to a mod 2 Moore space"J. Math. Kyoto Univ.. (印刷中).
[Publications] H.Shiga, K.Tsukiyama, T.Yamaguchi: "Principal S^1-bundles and forgetful maps"Contempprary Math.. 274. 293-297 (2001)
[Publications] Y.Kawamota, J.Lin: "Homotopy commutativity of H-spaces with finitely generated cohomology"Trans. Amer. Math. Soc.. 353. 4481-4496 (2001)
[Publications] Y.Kawamota: "Higher homotopy commutativity of H-spaces with finitely generated cohomology"Pacific J. Math.. (印刷中).

2001 Fiscal Year Annual Research Report

高次元多面体とoperadの研究

Principal Investigator

逸見 豊 高知大学, 理学部, 教授 (70181477)

Research Products

[Publications] Y.Hemmi: "Mod p decompositions of mod p finite H-spaces"Mem. Fac. Sci. Kochi Univ. Ser. A (Math.). 22. 59-65 (2001)

[Publications] Y.Hemmi, J.Lin: "Cohomology Rings of 3-local Finite H-spaces"J. Pure Appl. Algebra. (印刷中).

[Publications] Y.Hemmi: "Unstable p-th order operation and H-spaces"Contemporary Math.. (印刷中).

[Publications] Y.Kamiya, K.Shimomura: "The homotopy groups π_*(L_2V(0)∧T(k))"Hiroshima Math. J.. 31. 391-408 (2001)

[Publications] K.Shimomura, X.Wang: "The homotopy groups π_*(L_2S^0) at the prime 3"Topology. (印刷中).

[Publications] K.Shimomura: "The homotopy groups π_*(L_nT(m)∧V(n-2))"Contemporary Math.. (印刷中).

[Publications] K.Shimomura, X.Wang: "The Adams-Novikov E_2-term for π_*(L_2S^0) at the prime 2"Math. Z.. (印刷中).

[Publications] Y.Kamiya, K.Shimomura: "E_*-homology spheres for a connective spectrum E"Contemporary Math.. (印刷中).

[Publications] T.Kobayashi, K.Komatsu: "Extendibility and stable extendibility of vector bundles over real projective spaces"Hiroshima Math. J.. 31. 99-106 (2001)

[Publications] K.Komatsu: "Periods of cut-and-project tiling spaces from root lattices"Hiroshima Math. J.. 31. 435-438 (2001)

[Publications] S.Ishiguro, K.Komatsu: "Symmetries of cut-and-project tilings corresponding to exceptional folding"Mem. Fac. Sci. Koch Univ. (Math.). 22(印刷中). (2001)

[Publications] T.Kobayashi, K.Komatsu: "Extendibility and stable extendibility of the square of the normal bundle associated to an immersion of the real projective space"Hiroshima Math. J.. (印刷中).

[Publications] K.Morisugi: "Composition sturctnre of the self maps of SU(3) and Sp(2)"Contemporary Math.. 274. 233-240 (2001)

[Publications] K.Morisugi: "The Whitehead square of a lift of the Hopf map to a mod 2 Moore space"J. Math. Kyoto Univ.. (印刷中).

[Publications] H.Shiga, K.Tsukiyama, T.Yamaguchi: "Principal S^1-bundles and forgetful maps"Contempprary Math.. 274. 293-297 (2001)

[Publications] Y.Kawamota, J.Lin: "Homotopy commutativity of H-spaces with finitely generated cohomology"Trans. Amer. Math. Soc.. 353. 4481-4496 (2001)

[Publications] Y.Kawamota: "Higher homotopy commutativity of H-spaces with finitely generated cohomology"Pacific J. Math.. (印刷中).

逸見豊高知大学, 理学部, 教授 (70181477)