Janko Latschev
Lecture course Introduction to symplectic geometry, Wintersemester 2014/15
The lectures take place Tuesday and Thursday 8-10 in H5.
The exercise class has moved and now takes place Mondays 14-16 in room Geom 241.
Exams will take place on February 12/13 or March 26/27.
Other dates are possible by mutual agreement.
Here is a summary of the main exam topics, together with some general remarks concerning the exam.
The following books and lecture notes are useful study material for various parts of the course.
For background on manifolds, flows, Lie derivative, etc.:
| F. Warner | Foundations of differentiable manifolds and Lie groups | Springer Verlag |
| M. Spivak | A comprehensive introduction to differential geometry, vol. 1 | Publish or Perish |
| I. Madsen, J.Tornehave | From calculus to cohomology | Cambridge University Press |
For background on differential topology (tubular neighborhood theorem, intersection theory, etc.):
| J. Milnor | Topology from the differentiable viewpoint | The University of Virginia Press |
| V. Guillemin, A. Pollack | Differential topology | Prentice Hall |
| M. Hirsch | Differential topology | Springer Verlag |
For general topics in symplectic geometry:
| D. McDuff, D. Salamon | Introduction to symplectic topology | Oxford University Press |
| A. Canas da Silva | Lectures on Symplectic Geometry | Springer Lecture Notes in Mathematics 1764 |
| K. Cieliebak | Lectures on Symplectic Geometry, part A |
| H. Hofer, E. Zehnder | Symplectic Invariants and Hamiltonian dynamics | Birkhäuser |
| L. Polterovich | The Geometry of the Group of Symplectic Diffeomorphisms | Birkhäuser |
For some relations to physics:
| V.I. Arnold | Mathematical methods of classical mechanics | Springer Verlag |
| V. Guillemin, S. Sternberg | Symplectic techniques in physics | Cambridge University Press |
The exercise sheets will be posted here:
Sheet 1
Sheet 2
Sheet 3
Sheet 4
Sheet 5
Sheet 6 (corrected 11/29)
Sheet 7
Sheet 8 (corrected 12/10)
Sheet 9 (corrected 12/29, due 1/12/2015)
Sheet 10
Sheet 11
Other material will also appear here as needed.
Here is a short summary on the complexified tangent and cotangent bundles for almost complex and complex manifolds.
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