Nash Manifolds

  • Authors
  • Masahiro Shiota

Part of the Lecture Notes in Mathematics book series (LNM, volume 1269)

Table of contents

  1. Front Matter
    Pages I-VI
  2. Masahiro Shiota
    Pages 1-5
  3. Masahiro Shiota
    Pages 6-78
  4. Masahiro Shiota
    Pages 79-141
  5. Masahiro Shiota
    Pages 142-154
  6. Masahiro Shiota
    Pages 155-174
  7. Masahiro Shiota
    Pages 175-188
  8. Masahiro Shiota
    Pages 189-215
  9. Back Matter
    Pages 216-223

About this book

Introduction

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 This book, in which almost all results are very recent or unpublished, is an account of the theory of Nash manifolds, whose properties are clearer and more regular than those of differentiable or PL manifolds.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.

Keywords

differential topology manifold topology

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0078571
  • Copyright Information Springer-Verlag Berlin Heidelberg 1987
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-18102-6
  • Online ISBN 978-3-540-47763-1
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book