Janko Latschev
Lecture Course Differential Topology, Winter Semester 2017/18
Lectures take place on Tuesday 810 in H5 and on Thursday 810 in H4. There will be exercise classes Thursdays 1012 in Geom 142.
Prerequisites:  necessary: topology (including fundamental group and covering spaces), basics about manifolds (tangent bundle, flows of vector fields, differential forms)
 recommended: some differential geometry (Riemannian geometry, exponential map)
 also helpful: some algebraic topology (homology and cohomology)
There will be oral exams in the week immediately following the semester, i.e. starting February 5.
In differential topology we study the topology of differentiable manifolds and smooth maps between them. In this course we will start with a discussion of basics such as transversality and degree theory and their applications. We will also discuss vector bundles and tubular neighborhoods. Further topics will depend on audience interest and background knowledge, and may include classification questions for vector bundles, the construction of characteristic classes via ChernWeil theory, Morse theory and surgery constructions, and the ThomPontryagin construction.
The exercise sheets are published here:
Some useful references:
J. Milnor  Topology from the differentiable viewpoint  University Press of Virginia 
R. Bott, L. Tu  Differential Forms in Algebraic Topology  Springer Verlag 
M. Hirsch  Differential Topology  Springer Verlag 
A. Kosinski  Differential Manifolds  Academic Press 
I. Madsen, J. Tornehave  From calculus to cohomology  Cambridge University Press 
J. Robbin, D. Salamon  Introduction to Differential Topology  Book project 
