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SF2722,
Differential geometry, 7.5 hp, Spring 2009
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:
* Lectures on Tuesdays 10.15-12.00, room
3733, Department of Mathematics, KTH.
* Exercise session,
Tuesdays 9.15-10.00. Lectures:
Comments
on the lectures can be found in the course
log.
Literature
and course content: The
plan is to cover the course book with certain exceptions (the
exceptions include Chapters 9 and 11).
*
Conlon, ”Differentiable
manifolds”, Reprint of the 2001 2nd ed., 2008, ISBN:
978-0-8176-4766-7. Available at Kårbokhandeln,
Osquars Backe 21.
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).
*
Looijenga, ”Smooth Manifolds”, (lecture notes available
here)
*
Lee, ”Introduction to smooth manifolds”, (book)
Key
words: Differentiable manifolds and maps, tangent vectors,
flows of vector fields, Lie groups, differential forms, Stokes
theorem, de Rham cohomology, degree of a mapping, Riemannian
metrics, curvature.
Prerequisites:
SF2700,
Analysis, or corresponding background. This course follows
naturally ”Elementary
differential geometry” at Stockholm University, and it is
recommended to have taken this course. A good knowledge of
calculus of several variables and the inverse and implicit
function theorems is an important prerequisite.
Examination:
The examination will be in the form of homework problems
followed by an oral examination. For grades C-E you only have to
solve the homework problems. For grades A-B (and for graduate
students) you must also do the oral examination where you will
be asked to present details on your homework solutions and certain knowledge of the corresponding theory.
Homework
problems:
*
Homework
1.
* Homework
2.
* Homework
3.
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