Analytic and geometric study of stratified spaces / Markus J. PflaumType de document : MonographieCollection : Lecture notes in mathematics, 1768Langue : anglais.Pays : Allemagne.Éditeur : Berlin : Springer, 2001Description : 1 vol. (VIII-230 p.) : ill. ; 24 cmISBN : 9783540426264.ISSN : 0075-8434.Bibliographie : Bibliogr. p. -226. Index.Sujet MSC : 58A35, General theory of differentiable manifolds, Stratified sets
16E40, Homological methods in associative algebras, (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.)
14B05, Local theory in algebraic geometry, Singularities
13D03, Homological methods in commutative ring theory, (Co)homology of commutative rings and algebras
32S60, Complex singularities, Stratifications; constructible sheaves; intersection cohomology (complex-analytic aspects)En-ligne : Springerlink | Zentralblatt | MathSciNet
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Bibliogr. p. -226. Index
n this book, the author presents the deeper insight to the geometric-analytic structure of a stratified space. The monograph explains the theory of stratified spaces stating from the very beginning and therefore it fills the gap in the existing literature very well.
In the first chapter the author defines the basic notions of decompositions and stratifications together with the most important stratification conditions and introduces a meaningful functional structure on stratified spaces which is appropriate for analytic and geometric considerations.
In the second chapter it is shown that the functional structures introduced in the first chapter are suitable to do the differential geometry on stratified spaces. It is interesting to observe how many geometric structures can be transferred to stratified spaces with a smooth structure.
The third chapter is devoted to the control theory introduced by J. N. Mather. Mather’s ideas are supplemented by the notions of curvature moderate tubes and control data.
An important class of stratified spaces defined by orbit spaces is presented in Chapter 4. The fifth chapter presents the deRham theory on stratified spaces with a smooth structure, while the last chapter of the book deals with the topological Hochschild homology. (Zentralblatt)