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

DOI10.1016/S0166-8641(01)00200-0zbMath1028.57034OpenAlexW2058338127MaRDI QIDQ697618

Tomohiro Kawakami

Publication date: 17 September 2002

Published in: Topology and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0166-8641(01)00200-0

zbMATH Keywords

o-minimalcompactifiabledefinable \(C^rG\) manifoldsdefinable \(C^rG\) vector bundlesequivariant differential topologypiecewise definable \(C^r G\) trivality

Mathematics Subject Classification ID

Equivariant algebraic topology of manifolds (57R91) Compact Lie groups of differentiable transformations (57S15) Differential topology (57R99) Semialgebraic sets and related spaces (14P10) Differentiable manifolds, foundations (58A05) Topology of vector bundles and fiber bundles (57R22) Real-analytic and Nash manifolds (58A07) Model theory of ordered structures; o-minimality (03C64) Nash functions and manifolds (14P20)

Cites Work

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• One-dimensional Nash groups
• Nash manifolds
• On groups and fields definable in o-minimal structures
• Smooth conjugacy of algebraic actions on affine varieties
• Equivariant bundles
• Classification of Nash manifolds
• Expansions of the real field with power functions
• The elementary theory of restricted analytic fields with exponentiation
• Geometry of subanalytic and semialgebraic sets
• Nash \(G\) manifold structures of compact or compactifiable \(C^ \infty G\) manifolds
• The equivariant covering homotopy property for differentiable G-fibre bundles
• Geometric categories and o-minimal structures
• A theorem of the complement and some new o-minimal structures
• Equivariant differential topology
• Abstract Nash Manifolds
• The real field with convergent generalized power series
• Exponentiation is Hard to Avoid
• Model completeness results for expansions of the ordered field of real numbers by restricted Pfaffian functions and the exponential function

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