Analytic and geometric study of stratified spaces

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Analytic and geometric study of stratified spaces / Markus J. Pflaum

資料種別:: 図書
出版情報:: Berlin ; Tokyo : Springer, c2001
形態:: viii, 230 p. ; 24 cm
シリーズ名:: Lecture notes in mathematics ; 1768 <BA00146586>
著者名:: Pflaum, Markus J.
ISBN:: 9783540426264 [3540426264]
書誌ID:: BA54097757

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注記:

Includes bibliographical references (p. [215]-226) and index

主題:

Differentiable manifolds; Stratified sets

言語:

英語

目次情報:

Introduction

Notation

Stratified Spaces and Functional Structures / 1：

Decomposed spaces / 1.1：

Stratifications / 1.2：

Smooth Structures / 1.3：

Local Triviality and the Whitney conditions / 1.4：

The sheaf of Whitney functions / 1.5：

Rectifiable curves and regularity / 1.6：

Extension theory for Whitney functions on regular spaces / 1.7：

Differential Geometric Objects on Singular Spaces / 2：

Stratified tangent bundles and Whitney's condition (A) / 2.1：

Derivations and vector fields / 2.2：

Differential forms and stratified cotangent bundle / 2.3：

Metrics and length space structures / 2.4：

Differential Operators / 2.5：

Poisson structures / 2.6：

Control Theory / 3：

Tubular neighborhoods / 3.1：

Cut point distance and maximal tubular neighborhoods / 3.2：

Curvature moderate submanifolds / 3.3：

Geometric implications of the Whitney conditions / 3.4：

Existence and uniqueness theorems / 3.5：

Tubes and control data / 3.6：

Controlled vector fields and integrability / 3.7：

Extension theorems on controlled spaces / 3.8：

Thom's first isotopy lemma / 3.9：

Cone spaces / 3.10：

Orbit Spaces / 4：

Differentiable <$>\cal {G}<$>-Manifolds / 4.1：

Proper Group Actions / 4.2：

Stratification of the Orbit Space / 4.3：

Functional Structure / 4.4：

DeRham-Cohomology / 5：

The deRham complex on Singular Spaces / 5.1：

DeRham cohomology on <$>\cal {C}^\infty<$>-cone Spaces / 5.2：

DeRham theorems on orbit spaces / 5.3：

DeRham cohomology of Whitney functions / 5.4：

Homology of Algebras of Smooth Functions / 6：

Topological algebras and their modules / 6.1：

Homological algebra for topological modules / 6.2：

Continuous Hochschild homology / 6.3：

Hochschild homology of algebras of smooth functions / 6.4：

Supplements from linear algebra and functional analysis / A：

The vector space distance / A.1：

Polar decomposition / A.2：

Topological tensor products / A.3：

Kahler diflferentials / B：

The space of Kähler differentials / B.1：

Topological version / B.2：

Application to locally ringed Spaces / B.3：

Jets, Whitney functions and a few <$>\cal {C}^\infty<$>-mappings / C：

Fréchet topologies for <$>\cal {C}^\infty<$>-functions / C.1：

Jets / C.2：

Whitney functions / C.3：

Smoothing of the angle / C.4：

Introduction

Notation

Stratified Spaces and Functional Structures / 1：

Decomposed spaces / 1.1：

Stratifications / 1.2：

Smooth Structures / 1.3：

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