An element in the $n$th cobordism group $Nn(X)$ is represented by a map from an $n$-dimensional compact manifold without boundary into $X$. Two such maps are called bordant and represent the same element, if the two maps can be extended to a map on an $n+1$-dimensional manifold, whose boundary is the disjoint sum of the two $n$-dimensional manifolds. The funtor $N∗ ( - )$ that arises in this simple geometric fashion is a generalized homology theory. Already when $X$ is a point the group $N∗( pt)$ is interesting.
The aim of the seminar is to compute the bordism ring $N∗ ( pt )$. Along the way we will define many mathematical objects and learn to work with them: basic concepts from differential topology, the Pontrjagin-Thom construction, spectra, characteristic classes, formal groups, ...
Thedor Bröcker, Tammo tom Dieck: Kobordismentheorie, Lecture Notes in Mathematics 178, Springer-Verlag
Prerequisites: Familiarity with basic concepts of Algebraic Topology
A3/SR 210 Seminarraum
wöchentlich, ab 09.04.2019, 14:00 - 16:00 (14 Termine)