Rutgers university, new brunswick, new jersey 08903 and felix browder rutgers university, new brunswick, new jersey 08903 received september 11, 1997 contents 1. Morse theory has provided the inspiration for exciting developments in differential topology by s. They present some topics from the beginnings of topology, centering about l. S4d2 graduate seminar on topology morse theory s2d3. S2d3 hauptseminar differentialtopologie morsetheorie. Differential topology is the study of differentiable manifolds and maps. These problems do not belong so much to the realm of pure homotopy theory as to a special kind of homotopy theory connected with vector space bundles and the like, as exemplified by work around the bott periodicity theorems. Morse theory and the euler characteristic daniel mitsutani abstract. We then use the basics of morse theory and the poincar ehopf theorem to prove that the euler characteristic equals the sum of the alternating betti. Soon after winning the fields medal in 1962, a young john milnor gave these nowfamous lectures and wrote his timeless topology from the differentiable viewp.
Introduce an important and oftenused technique in differential topology. The methods used, however, are those of differential topology, rather. I have tried to describe some of this work in lectures on the hcobordism. The first was to give an introduction to morse theory from a topological point of view. Morse theory has provided the inspiration for exciting developments in differential topology by. A related slicing technique was employed in the study of the topology of algebraic manifolds called the picardlefschetz theory. Bott, morse theory and its application to homotopy theory. M is a critical point of f if the differential dfp. Brouwers definition, in 1912, of the degree of a mapping. Preface these lectures were delivered at the university of virginia in december 1963 under the sponsorship of the pagebarbour lecture foundation.
Morse a nd in the b o ok lectures on t he h cob ordism theorem b y j. About the book the present course deals with the fundamentals of. In this post we will see a course of differential geometry and topology a. He is the author of topology from the differential viewpoint, singular points of complex hypersurfaces, morse theory, introduction to algebraic k theory, characteristic classes with james stasheff, and lectures on the hcobordism theorem princeton. Differential topology, the subject of this paper, is the study of intrinsic topo logical properties of manifolds endowed with a smooth structure. On the one hand, morse theory is extremely important in the classi cation programme of manifolds. An invitation to morse theory university of notre dame.