Teacher: Mattias Dahl, dahl@math.kth.se, room 3630, Lindstedsv. 25, 790 65 88.
Course secretary: Rose-Marie Jansson, jansson@math.kth.se, room 3527, Lindstedsv. 25, 790 72 01
Time
and place: The lectures take place tuesdays, 10-12, in seminar
room 3733 at the mathematics department.
There will be no
lecture easter week, tuesday 3/4.
The course and all
examinations will be finished around the beginning of June.
Literature:
*
Barden, Thomas, ”An introduction to differential manifolds”
(available at Kårbokhandeln).
* Additional material on
Riemannian geometry.
Additional reading:
*
Warner, ”Foundations of Differentiable Manifolds and Lie
Groups”,
* Boothby, ”An Introduction to Differentiable
Manifolds and Riemannian Geometry”,
(both available here).
*
Hitchin, ”Differentiable Manifolds”, (lecture notes available
here).
Course content: The plan is to cover the entire content of the course book, except sections marked with *. Hopefully there will also be time for a short introduction to Riemannian geometry and curvature. In detail this means: Differentiable manifolds and maps, tangent vectors, vector bundles, differential forms, Stokes theorem, de Rham cohomology, degree of a mapping, Riemannian metrics, curvature.
Prerequisites: 5B1303, Analysis, or corresponding background.
Examination:
To pass the course it is required that you solve (essentially) all
the homework problems. Further you must do an oral examination (or
rather discussion) as follows.
* For grade 3/G/C you must be
able to explain your solutions to the homework problems and some
background details,
* For grade 5/VG/A (and for graduate
students) you must also be able to present solutions to all
exercises in the course book, and perhaps some deeper understanding
of theory and concepts.
I will not set any deadline for the
examination (at least not for a year or so). But I will be away from
2 june until midsummer. So either you can do the oral exam before
2/6, or after 25/6.
* Homework
problems 1,
to be handed in 13/2.
* Homework
problems 2,
to be handed in 6/3.
*
Homework
problems 3,
to be handed in 10/4.
* Homework
problems 4,
to be handed in 1/5.
* Homework
problems 5,
to be handed in 1/5.
Here
list of results (with names coded by initials.)
Lectures: Comments on the lectures are here.