Bordisms

Inhaltsangabe / Literatur / empfohlene Vorkenntnisse A first course in algebraic topology and some familiarity with smooth manifolds. List of references for the course T. Bröcker and T. tom Dieck, Kobordismentheorie, Springer Lecture Notes in Mathematics Vol. 178, Springer-Verlag, 1970. M. W. Hirsch, Differential topology, Graduate Texts in Mathematics No. 33, Springer-Verlag, 1976. A. A. Kosinski, Differential manifolds, Pure and Applied Mathematics No. 138, Academic Press, 1993. J. W. Milnor and J. D. Stasheff, Characteristic classes, Annals of Mathematical Studies No. 76, Princeton University Press, 1974. R. E. Stong, Notes on cobordism theory, Mathematical Notes Princeton University Press, 1968. R. W. Switzer, Algebraic topology - Homology and Homotopy, Die Grundlehren der mathematischen Wissenschaften Vol. 212, Springer-Verlag, 1975.

Course description This will be a course on cobordism theory. The aim of the course will be twofold (as is the theory itself): to give an introduction to differential topology and discuss the cobordism relation, an equivalence relation between closed smooth manifolds which leads to a (co)homology theory of spaces, and to develop the necessary tools from stable homotopy theory and the theory of characteristic classes in order to obtain some calculations of cobordism groups.