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Y.-H. Wan

Chapter 16 in From Topology to Computation: Proceedings of the Smalefest, 1993, pp 162-162 from Springer

Abstract: Abstract I would like to make a brief comment on a mathematical problem motivated by economics. Probably I am the first student of Stephen Smale in mathematical economics. My thesis was on Morse theory for two functions. The Morse theory for a single function on a manifold M can be regarded as a globalization of the studies on optimizing this single function. One obtains the so-called Morse inequalities. Following this viewpoint, one can also get a Morse theory for two functions f = (f1, f2): M → R2 as a globalization of the studies on optimizing two functions. In particular, one can obtain a suitable version of the Morse inequalities. Clearly, Smale’s idea about Morse theory for two functions shows a connection between this morning’s talks on differential topology and this afternoon’s talks on mathematical economics.

Keywords: Mathematical Problem; Cell Complex; Single Function; Morse Theory; Mathematical Economic (search for similar items in EconPapers)
Date: 1993
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-2740-3_16

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DOI: 10.1007/978-1-4612-2740-3_16

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