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Topological Classification of Morse Functions and Generalisations of Hilbert’s 16-th Problem

Arnold, Vladimir (2007), Topological Classification of Morse Functions and Generalisations of Hilbert’s 16-th Problem, Mathematical Physics Analysis and Geometry, 10, 3, p. 227-236. http://dx.doi.org/10.1007/s11040-007-9029-0

Type
Article accepté pour publication ou publié
Date
2007
Journal name
Mathematical Physics Analysis and Geometry
Volume
10
Number
3
Publisher
Springer
Pages
227-236
Publication identifier
http://dx.doi.org/10.1007/s11040-007-9029-0
Metadata
Show full item record
Author(s)
Arnold, Vladimir
Abstract (EN)
The topological structures of the generic smooth functions on a smooth manifold belong to the small quantity of the most fundamental objects of study both in pure and applied mathematics. The problem of their study has been formulated by A. Cayley in 1868, who required the classification of the possible configurations of the horizontal lines on the topographical maps of mountain regions, and created the first elements of what is called today ‘Morse Theory’ and ‘Catastrophes Theory’. In the paper we describe this problem, and in particular describe the classification of Morse functions on the 2 sphere and on the torus.
Subjects / Keywords
topological structure; generic smooth functions

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