Misc - KAWAKAMI Tomohiro

Every compactifiable C∞ manifold admits uncountably many algebraic models.

Bulletin of Faculty of Education Wakayama University, Natural Science.   55   21-22.   2005

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

A note on geometric educations in Faculty of Education Wakayama University

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

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

Kawakami Tomohiro

RIMS Kokyuroku ( Kyoto University )  1393   102 - 105   2004.09

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

Transformation groups and semi-groups.

Tomohiro kawakami

Encyclopedia of General Topology.     379-385.   2004

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

Kawakami Tomohiro

RIMS Kokyuroku ( Kyoto University )  1343   31 - 45   2003.10

Homotopy property for definable fiber bundles.

Tomohiro kawakami

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

Affineness of definable C^r manifolds and its applications.

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

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

Kawakami Tomohiro

RIMS Kokyuroku ( Kyoto University )  1290   121 - 126   2002.10

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

Tomohiro Kawakami

Topology and its Applications   123 ( 2 ) 323 - 349   2002.09

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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

Myung-Jun Choi, Tomohiro Kawakami, Dae Heui Park

Topology and its Applications   123 ( 2 ) 383 - 400   2002.09

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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 semialgebraic vector bundles

MJ Choi, T Kawakami, DH Park

TOPOLOGY AND ITS APPLICATIONS ( ELSEVIER SCIENCE BV )  123 ( 2 ) 383 - 400   2002.09

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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   2002.09

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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

Relative algebraic realizations of a closed C^∞G Manifold and its closed C^∞G sabmanifolb

川上 智博

Bull.Fac.Edu.Wakayama Univ. ( 和歌山大学教育学部 )  1-15   1 - 15   2002

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

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

(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

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

川上 智博

Bulletin of the Faculty of Education,Wakayama University. Natural science ( 和歌山大学教育学部 )  51   1 - 10   2001

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