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Differential Geometry II (Winter 15)
– Analysis and geometry on manifolds –
This course is a BMS basic course and the lectures will be in English. Please feel free to ask any questions (and to turn in any work) in English or German.
- Oral exams
will be offered on Friday 20 May and on Friday 3 June.
Differentiable manifolds, vector bundles, differential forms, Riemannian geometry.
Here is the revised 2015/6 version of Prof. Sullivan's
Please email Prof. Sullivan with any suggestions for corrections or improvements to these lecture notes.
Note that the course Differential Geometry I (Curves and Surfaces) is
not strictly a prerequisite for this course. It gives useful geometric
insight on the lower dimensional cases but is logically independent:
the courses can be taken in either order. For reference, here are the
lecture notes from last semester's course.
- Exercise sheet 1, due 26 October
- Exercise sheet 2, due 2 November
- Exercise sheet 3, due 9 November
- Exercise sheet 4, due 16 November
- Exercise sheet 5, due 23 November
- Exercise sheet 6, due 30 November
- Exercise sheet 7, due 7 December
- Exercise sheet 8, due 14 December
- Exercise sheet 9, due 11 January
- Exercise sheet 10, due 18 January
- Exercise sheet 11, due 25 January
- Exercise sheet 12, due 1 February
- Kühnel, Differential Geometry / Differentialgeometrie, AMS / Vieweg
- Boothby, An Introduction to Differentiable Manifolds and Riemannian Geometry, 2nd Ed, Academic Press
- Bröcker and Jänich, Introduction to Differential Topology / Einführung in die Differentialtopologie, CUP / Springer
- Warner, Foundations of Differentiable Manifolds and Lie Groups, GTM 94, Springer
- Morgan, Riemannian Geometry: A Beginner's Guide, 2nd Ed, A K Peters
- Bishop and Goldberg, Tensor Analysis on Manifolds, Dover
- Milnor, Topology from the Differentiable Viewpoint, U P Virginia
- Spivak, Calculus on Manifolds, Benjamin/Cummings
- Sharpe, Differential Geometry, GTM 166, Springer
Homework should be turned in by groups of two students.
To get a certificate for the tutorial and qualify to take the oral exam at the end of the semester, you need to satisfactorily complete 60% of the homework assignments.
||Prof. John Sullivan
||Thu 13:30–14:30||MA 802
||by appointment||MA 882
||Mon, Tue, Thu, Fri 9:30–11:30||MA 803