Pflaum Analytic and Geometric Study of Stratified Spaces

Contributions to Analytic and Geometric Aspects
2001
ISBN: 978-3-540-45436-6
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 1768, 234 Seiten, eBook

Reihe: Lecture Notes in Mathematics

Zielgruppe

Research

Autoren/Hrsg.

Pflaum, Markus J.

Inhaltsverzeichnis

Introduction Notation 1 Stratified Spaces and Functional Structures 1.1 Decomposed spaces 1.2 Stratifications 1.3 Smooth Structures 1.4 Local Triviality and the Whitney conditions 1.5 The sheaf of Whitney functions 1.6 Rectifiable curves and regularity 1.7 Extension theory for Whitney functions on regular spaces 2 Differential Geometric Objects on Singular Spaces 2.1 Stratified tangent bundles and Whitney's condition (A) 2.2 Derivations and vector fields 2.3 Differential forms and stratified cotangent bundle 2.4 Metrics and length space structures 2.5 Differential operators 2.6 Poisson structures 3 Control Theory 3.1 Tubular neighborhoods 3.2 Cut point distance and maximal tubular neighborhoods 3.3 Curvature moderate submanifolds 3.4 Geometric implications of the Whitney conditions 3.5 Existence and uniqueness theorems 3.6 Tubes and control data 3.7 Controlled vector fields and integrability 3.8 Extension theorems on controlled spaces 3.9 Thom's first isotopy lemma 3.10 Cone spaces 4 Orbit Spaces 4.1 Differentiable G-Manifolds 4.2 Proper Group Actions 4.3 Stratification of the Orbit Space 4.4 Functional Structure 5 DeRham-Cohomology 5.1 The deRham complex on singular spaces 5.2 DeRham cohomology on C^/infty-cone spaces 5.3 DeRham theorems on orbit spaces 5.4 DeRham cohomology of Whitney functions 6 Homology of Algebras of Smooth Functions 6.1 Topological algebras and their modules 6.2 Homological algebra for topological modules 6.3 Continuous Hochschild homology 6.4 Hochschild homology of algebras of smooth functions A Supplements from linear algebra and functional analysis A.1 The vector space distance A.2 Polar decomposition A.3 Topological tensor products B Kähler differentials B.1 The space of Kähler differentials B.2 Topological version B.3 Application to locally ringed spaces C Jets, Whitney functions and a few C^/infty -mappings C.1 Frechet topologies for C^/infty -functions C.2 Jets C.3 Whitney functions C.4 Smoothing of the angle