The book provides an introduction to stratification theory leading the reader up to modern research topics in the field. The first part presents the basics of stratification theory, in particular the Whitney conditions and Mather's control theory, and introduces the notion of a smooth structure. Moreover, it explains how one can use smooth structures to transfer differential geometric and analytic methods from the arena of manifolds to stratified spaces. In the second part the methods established in the first part are applied to particular classes of stratified spaces like for example orbit spaces. Then a new de Rham theory for stratified spaces is established and finally the Hochschild (co)homology theory of smooth functions on certain classes of stratified spaces is studied. The book should be accessible to readers acquainted with the basics of topology, analysis and differential geometry.
Analytic and Geometric Study of Stratified Spaces
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Inside This Book
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First Sentence:
Let X be a paracompact Hausdorff space with countable topology, and Z a locally finite partition of X into locally closed subspaces S C X. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
singular atlas, global singular chart, singular charts, inner metric space, proper control data, symplectic stratified spaces, controlled submersion, stratified subspace, vector space distance, formality theorem, decomposed space, kernel bundle, compact exhaustion, controlled vector fields, first isotopy lemma, subanalytic sets, locally convex algebra, tubular neighborhood theorem, sheaf complex, normal control data, valued section, smooth structure, local triviality, metric cones, generalized lemma Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proposition Let, Definition Let, Example Let, Corollary Let, Example Every, Jim Etx, Levi Civita, Remark One, Riemannian Whitney New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Let X be a paracompact Hausdorff space with countable topology, and Z a locally finite partition of X into locally closed subspaces S C X. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
singular atlas, global singular chart, singular charts, inner metric space, proper control data, symplectic stratified spaces, controlled submersion, stratified subspace, vector space distance, formality theorem, decomposed space, kernel bundle, compact exhaustion, controlled vector fields, first isotopy lemma, subanalytic sets, locally convex algebra, tubular neighborhood theorem, sheaf complex, normal control data, valued section, smooth structure, local triviality, metric cones, generalized lemma Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proposition Let, Definition Let, Example Let, Corollary Let, Example Every, Jim Etx, Levi Civita, Remark One, Riemannian Whitney New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 75
books:
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- Forward-Backward Stochastic Differential Equations and their Applications (Lecture Notes in Mathematics) by Jin Ma in Back Matter (1), and Back Matter (2)
- An Introduction to Homological Algebra (Cambridge Studies in Advanced Mathematics) by Charles A. Weibel in Back Matter
- Sheaves on Manifolds: With a Short History "Les debuts de la theorie des faisceaux" by Christian Houzel (Grundlehren der mathematischen Wissenschaften) by Masaki Kashiwara in Back Matter
- Variational Methods for Problems from Plasticity Theory and for Generalized Newtonian Fluids (Lecture Notes in Mathematics) by Martin Fuchs in Back Matter
- Flows on 2-dimensional Manifolds: An Overview (Lecture Notes in Mathematics) by Igor Nikolaev in Back Matter
See all 75 books this book cites
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