ENGLISH

Nash Manifolds

By Masahiro Shiota (auth.)

Book information

Publisher
Springer-Verlag Berlin Heidelberg
Year
1987
ISBN
9780387181028, 0-387-18102-4
DOI
10.1007/BFb0078571
LCC
QA3 .L28 no. 1269,QA614.3 .L28 no. 1269
Open Library ID
OL2387604M
Language
english
Format
DJVU
Filesize
1 MB (1378862 bytes)
Series
Lecture Notes in Mathematics 1269
Edition
1
Pages
228\234
Library
mexmat
Time added
2009-07-20 03:45:11
Manifolds and Cell Complexes (incl. Diff.Topology)

Description

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 This book, in which almost all results are very recent or unpublished, is an account of the theory of Nash manifolds, whose properties are clearer and more regular than those of differentiable or PL manifolds.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