Misc - 川上　智博

Equivariant definable C^r approximation theorem, definable C^r G triviality of definable C^r G maps and Nash G compactifications.

Bulletin of Faculty of Education Wakayama University, Natural Science.   55   23 - 36   2005年

和歌山大学教育学部における幾何学教育についての考察

川上 智博

和歌山大学教育学部教育実践総合センター紀要.   15   83 - 84   2005年

DEFINABLE $C^rG$ TRIVIALITY OF $G$ INVARIANT PROPER DEFINABLE $C^r$ MAPS (Transformation Group Theory and Surgery)

川上 智博

数理解析研究所講究録 ( 京都大学 )  1393   102 - 105   2004年09月

Definable G CW complex structures of definable G sets and their applications.

Bulletin of Faculty of Education Wakayama University, Natural Science.   54   1-15.   2004年

Transformation groups and semi-groups.

Tomohiro kawakami

Encyclopedia of General Topology.     379-385.   2004年

DEFINABLE $G$-FIBER BUNDLES AND DEFINABLE $C^rG$-FIBER BUNDLES (Topological Transformation Groups and Related Topics)

川上 智博

数理解析研究所講究録 ( 京都大学 )  1343   31 - 45   2003年10月

Homotopy property for definable fiber bundles.

Tomohiro kawakami

Bulletin of Faculty of Education Wakayama University, Natural Science.   53   1 - 6   2003年

Affineness of definable C^r manifolds and its applications.

Bulletin of the Korean Mathematical Society.   40   149 - 157   2003年

DEFINABLE FIBER BUNDLES AND AFFINENESS OF DEFINABLE $C^r$ MANIFOLDS (Transformation groups from new points of view)

川上 智博

数理解析研究所講究録 ( 京都大学 )  1290   121 - 126   2002年10月

Equivariant semialgebraic vector bundles

Myung-Jun Choi, Tomohiro Kawakami, Dae Heui Park

Topology and its Applications   123 ( 2 ) 383 - 400   2002年09月

　概要を見る

Let G be a compact semialgebraic group. We prove that any semialgebraic G-vector bundle over a semialgebraic G-set has a semialgebraic classifying G-map. Moreover we prove that the set of semialgebraic G-isomorphism classes of semialgebraic G-vector bundles over a semialgebraic G-set corresponds bijectively to the set of topological G-isomorphism classes of topological G-vector bundles over it. As an application of them, we prove that for any two semialgebraic G-maps f,h between semialgebraic G-sets M and N, if they are G-homotopic and ξ is a semialgebraic G-vector bundle over N, then f*(ξ) and h*(ξ) are semialgebraically G-isomorphic. © 2001 Elsevier Science B.V. All rights reserved.

DOI

Equivariant differential topology in an o-minimal expansion of the field of real numbers

Tomohiro Kawakami

Topology and its Applications   123 ( 2 ) 323 - 349   2002年09月

　概要を見る

We establish basic properties of differential topology for definable CrG manifolds in an o-minimal expansion M of ℝ(ℝ,+,·,&lt
), where 0≤r≤ω and G is a definable Cr group. © 2002 Elsevier Science B.V. All rights reserved.

DOI

Equivariant semialgebraic vector bundles

MJ Choi, T Kawakami, DH Park

TOPOLOGY AND ITS APPLICATIONS ( ELSEVIER SCIENCE BV )  123 ( 2 ) 383 - 400   2002年09月

　概要を見る

Let G be a compact semialgebraic group. We prove that any semialgebraic G-vector bundle over a semialgebraic G-set has a semialgebraic classifying G-map. Moreover we prove that the set of semialgebraic G-isomorphism classes of semialgebraic G-vector bundles over a semialgebraic G-set corresponds bijectively to the set of topological G-isomorphism classes of topological G-vector bundles over it. As an application of them, we prove that for any two semialgebraic G-maps f, h between semialgebraic G-sets M and N, if they are G-homotopic and xi is a semialgebraic G-vector bundle over N, then f *(xi) and h*(xi) are sernialgebraically G-isomorphic. (C) 2001 Elsevier Science B.V. All rights reserved.

DOI

Equivariant differential topology in an o-minimal expansion of the field of real numbers

T Kawakami

TOPOLOGY AND ITS APPLICATIONS ( ELSEVIER SCIENCE BV )  123 ( 2 ) 323 - 349   2002年09月

　概要を見る

We establish basic properties of differential topology for definable C(r)G manifolds in an o-minimal expansion M of R = (R, +, ., <), where 0 less than or equal to, r less than or equal to, omega and G is a definable C-r group. (C) 2002 Elsevier Science B.V. All rights reserved.

DOI

閉G多様体とその閉G部分多様体の同時代的実現について

川上 智博

和歌山大学教育学部紀要 自然科学 ( 和歌山大学教育学部 )  1-15   1 - 15   2002年

閉C^∞G多様体とその閉C^∞G部分多様体の対代数的現実について.

    2002年

代数的,半代数的およびデファイナブルカテゴリーにおけるG多様体とGベクトル束について

予定     2001年

(R,t.・,c)への順序極小拡張での同変微分トポロジーについて

    2001年

ベクトル束の代数的,Nash実現と同変Nashおよび代数的ベクトル束の自明性について

川上 智博

和歌山大学教育部紀要 ( 和歌山大学教育学部 )  51   1 - 10   2001年

Algebraic and Nash realizations of vector bundles, and triviality of equivariant algebraic and Nash rector bundles.

Bull. Fac. Edu. Natur. Sci. Wakayama University   51   1 - 10   2001年

G多様体の局所Nash構造について

川上 智博

和歌山大学教育学部紀要 自然科学 ( 和歌山大学教育学部 )  50 ( 50 ) 1 - 16   2000年