Morse functions and the theorem about the Euler characteristic
No. 142, 1975
(Analysis on manifolds, function theory)
India ink and pencil on paper, 30.5x42.5 cm.
A gelatinous ice-palace, bursting through the surface of an energetic sea, rises skyward almost as if gravity were tugging it from the black heavens above. This image illustrates a typical graph of a smooth function, in which all of its critical points are nondegenerate, otherwise known as a Morse function. Notice that the basic shapes of the critical points— maxima, minima, and saddle points—are easily seen on a common landscape as peaks, valleys, and passes. As it turns out, the number and type of critical points of a function largely determine the topology of the space in which it is defined. It is this connection that makes up the subject of Morse theory, which is also the core idea of this picture.
