Nash Manifolds [electronic resource] / by Masahiro Shiota.
Material type: TextSeries: Lecture Notes in Mathematics ; 1269Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 1987Description: VIII, 228 p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783540477631Subject(s): Mathematics | Cell aggregation -- Mathematics | Mathematics | Manifolds and Cell Complexes (incl. Diff.Topology)Additional physical formats: Printed edition:: No titleDDC classification: 514.34 LOC classification: QA613-613.8QA613.6-613.66Online resources: Click here to access onlineCurrent library | Home library | Call number | Materials specified | URL | Status | Date due | Barcode |
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IMSc Library | IMSc Library | Link to resource | Available | EBK1608 |
Preliminaries -- Approximation theorem -- Affine Cr nash manifolds -- Nonaffine C? nash manifolds -- C0 nash manifolds -- Affine C? nash manifolds.
A Nash manifold denotes a real manifold furnished with algebraic structure, following a theorem of Nash that a compact differentiable manifold can be imbedded in a Euclidean space so that the image is precisely such a manifold. This book, in which almost all results are very recent or unpublished, is an account of the theory of Nash manifolds, whose properties are clearer and more regular than those of differentiable or PL manifolds. Basic to the theory is an algebraic analogue of Whitney's Approximation Theorem. This theorem induces a "finiteness" of Nash manifold structures and differences between Nash and differentiable manifolds. The point of view of the author is topological. However the proofs also require results and techniques from other domains so elementary knowledge of commutative algebra, several complex variables, differential topology, PL topology and real singularities is required of the reader. The book is addressed to graduate students and researchers in differential topology and real algebraic geometry.
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