Abstract
A surface is a two-dimensional manifold. The classification of compact surfaces was “known,” in some sense, by the end of the nineteenth century. Möbius [1] and Jordan [1] offered proofs (for orientable surfaces in ℝ3) in the 1860’s. Möbius’ paper is quite interesting; in fact he used a Morse-theoretic approach similar to the one presented in this chapter. The main interest in Jordan’s attempt is in showing how the work of an outstanding mathematician can appear nonsensical a century later.
Un des problèmes centraux posés à l’esprit humain est le problème de la succession des formes.
R. Thom, Stabilité Structurelle et Morphogénèse, 1972
Concerned with forms we gain a healthy disrespect for their authority ...
M. Shub, For Ralph, 1969
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© 1976 Springer-Verlag New York Inc.
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Hirsch, M.W. (1976). Surfaces. In: Differential Topology. Graduate Texts in Mathematics, vol 33. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-9449-5_10
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DOI: https://doi.org/10.1007/978-1-4684-9449-5_10
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