Saturday, September 15, 2018

Download An Introduction to Morse Theory (Translations of Mathematical Monographs, Vol. 208) (pdf) by Yukio Matsumoto


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In a very broad sense, "spaces" are objects of study in geometry, and "functions" are objects of study in analysis. There are, however, deep relations between functions defined on a space and the shape of the space, and the study of these relations is the main theme of Morse theory. In particular, its feature is to look at the critical points of a function, and to derive information on the shape of the space from the information about the critical points..
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