Analytic and Geometric Study of Stratified Spaces: Contributions to Analytic and Geometric Aspects: 1768 (Lecture Notes in Mathematics, 1768) - Softcover

Pflaum, Markus J.

Softcover

ISBN 10: 3540426264 ISBN 13: 9783540426264

Publisher: Springer, 2001

Synopsis

stratified collectionsofdiffer- inamore intuitive are Expressed terminology, spaces in This characteristic tiable manifoldswhich are an glued together appropriate way. of manifolds" feature becomes in the name or original "complexes [188] apparent of "manifold collections" See. HASSLERWHITNEY fora the by predecessor [189, 11) of stratified WHITNEY's article from the 1947 modern notion a [188] space. year the birth date of abstract of stratifications. Nev- can be as an theory regarded have considered before 1947 which mathematicians nowadays theless, already topics, of stratified like for at theend ofthe are treated within the theory spaces, example to when nineteenth when or century, algebraic geometers began study singularities and of varieties The interest in simplicialcomplexes triangulations algebraic began. of manifolds" in for the introduction of the so-called was reason "complexes [188] bounded submanifold of the observation that the of a some boundary noncompact lower dimensional Euclidean oftenbe in can decomposed locally finitelymany space inmodern manifolds. This ofviewhasbeentaken point again geometric analysis up and for instance forms the basis of the of a or a concept manifold-with-boundary manifold-with-corners for MELROSE or RENETHOM example [126, 127] 1.1.19). (see noticed in his work of 1955 that his iterated sets of of asmooth singularities [1661 f R' R' manifolds for certain functions and a : -4 are generic comprise mapping collection" inthe ofWHITNEY WHITNEY 1957in "manifold sense proved [190] [1891.

About this title

Synopsis

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.

Edition details

• Publisher: Springer
• Publication date: 2001
• Language: English
• ISBN 10: 3540426264
• ISBN 13: 9783540426264
• Binding: Paperback
• Number of pages: 244