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Convex Integration Theory - Solutions to the h-principle in geometry and topology (Paperback, Softcover reprint of the original 1st ed. 1998)
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Convex Integration Theory - Solutions to the h-principle in geometry and topology (Paperback, Softcover reprint of the original 1st ed. 1998)
Series: Monographs in Mathematics, 92
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1. Historical Remarks Convex Integration theory, first introduced
by M. Gromov [17], is one of three general methods in
immersion-theoretic topology for solving a broad range of problems
in geometry and topology. The other methods are: (i) Removal of
Singularities, introduced by M. Gromov and Y. Eliashberg [8]; (ii)
the covering homotopy method which, following M. Gromov's thesis
[16], is also referred to as the method of sheaves. The covering
homotopy method is due originally to S. Smale [36] who proved a
crucial covering homotopy result in order to solve the
classification problem for immersions of spheres in Euclidean
space. These general methods are not linearly related in the sense
that succes sive methods subsumed the previous methods. Each method
has its own distinct foundation, based on an independent
geometrical or analytical insight. Conse quently, each method has a
range of applications to problems in topology that are best suited
to its particular insight. For example, a distinguishing feature of
Convex Integration theory is that it applies to solve closed
relations in jet spaces, including certain general classes of
underdetermined non-linear systems of par tial differential
equations. As a case of interest, the Nash-Kuiper Cl-isometrie
immersion theorem ean be reformulated and proved using Convex
Integration theory (cf. Gromov [18]). No such results on closed
relations in jet spaees can be proved by means of the other two
methods.
General
Imprint: |
Birkhauser Verlag AG
|
Country of origin: |
Switzerland |
Series: |
Monographs in Mathematics, 92 |
Release date: |
August 2014 |
First published: |
1998 |
Editors: |
David Spring
|
Dimensions: |
235 x 155 x 12mm (L x W x T) |
Format: |
Paperback
|
Pages: |
213 |
Edition: |
Softcover reprint of the original 1st ed. 1998 |
ISBN-13: |
978-3-03-489836-2 |
Categories: |
Books >
Science & Mathematics >
Mathematics >
Topology >
General
|
LSN: |
3-03-489836-3 |
Barcode: |
9783034898362 |
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