Dietmar A. Salamon: Catalogue data in Spring Semester 2018 |
| Name | Prof. em. Dr. Dietmar A. Salamon |
| Address | Dep. Mathematik ETH Zürich, HG G 50.1 Rämistrasse 101 8092 Zürich SWITZERLAND |
| dietmar.salamon@math.ethz.ch | |
| URL | http://www.math.ethz.ch/~salamon |
| Department | Mathematics |
| Relationship | Professor emeritus |
| Number | Title | ECTS | Hours | Lecturers | |
|---|---|---|---|---|---|
| 401-3532-08L | Differential Geometry II  | 10 credits | 4V + 1U | D. A. Salamon | |
| Abstract | Introduction to Differential Topology, including degree theory and intersection theory; Differential forms, including deRham cohomology and Poincare duality; Vector bundles, including Thom isomorphism and Euler number. | ||||
| Learning objective | The aim of this course is to give an introduction to Differential Topology including the degree of a mapping and intersection theory, differential forms including deRham cohomology and Poincare duality, and vector bundles including the Thom isomorphism theorem. | ||||
| Content | Introduction to Differential Topology, including the mod-2 degree, orientation and the Brouwer degree, Poincare-Hopf Theorem, the Pontryagin construction, Hopf Degree Theorem., intersection theory, Lefschetz numbers; Differential forms, Stokes, Cartan's formula, deRham cohomology, Mayer-Vietoris, Poincare duality, Euler characteristic, Degree Theorem, Gauss-Bonnet, Moser isotopy, Cech-DeRham complex and finite-dimensionality; Vector bundles, Thom isomorphism, Euler number. | ||||
| Literature | - J. Milnor, Topology from the Differential Viewpoint. Univ Virginia Press, 1969. - V. Guillemin, A. Pollack, Differential Topology. Prentice-Hall, 1974. - R. Bott, L.W. Tu, Differential Forms in Algebraic Topology, Springer, 1982. - J. Robbin, D. Salamon, Introduction to Differential Topology, in preparation. https://people.math.ethz.ch/~salamon/PREPRINTS/difftop.pdf | ||||
| Prerequisites / Notice | Prerequisite is a working knowledge of the introductory material in Differential Geometry I, including smooth manifolds, tangent bundles, vector fields and flows. see https://people.math.ethz.ch/~salamon/PREPRINTS/diffgeo.pdf | ||||
| 401-5350-00L | Analysis Seminar | 0 credits | 1K | M. Struwe, A. Carlotto, F. Da Lio, A. Figalli, N. Hungerbühler, T. Kappeler, T. Rivière, D. A. Salamon | |
| Abstract | Research colloquium | ||||
| Learning objective | |||||
| Content | Research seminar in Analysis | ||||
| 401-5580-00L | Symplectic Geometry Seminar | 0 credits | 2K | D. A. Salamon, P. Biran | |
| Abstract | Research colloquium | ||||
| Learning objective | |||||