The exam on Differentiable Manifolds
Monday
January 31 from 14:00-17:00
in
the Educatorium Beta room
You can make your choice between:
- second part of the exam (only if you participated in the first part
in the fall of 2004)
- full exam.
In
both cases you have to register your name in OSIRIS in time before the
exam.
The lectures during
the second period are the subject of the second part exam:
This corresponds to: lecture notes Meetkunde
op Varieteiten (Looijenga)
*chapter
8 to 12 (included)
* voortgezette lineaire
algebra (extended linear algebra) section 3 :orientation
and internal contraction
* The hand-out:
More about Stokes (10 pages)
*
exercises from the second
period exercise sessions.
For
the full-exam one has to add the
subjects of the first period(which
were part of the first exam):
* chapter 1 to 7 (included)
* voortgezette lineaire
algebra (extended linear algebra) sections 1 to 3 (included)
(but without orientation and internal contraction)
* exercises
from the first period exercise sessions.
You may do the exam either in Dutch or in English. Books or notes may not be consulted.
Cross-references
with the book
:
T. Frankel : The Geometry of Physics
The course
fromLooijenga's notes [Lo] treat more or less
the same subjects as listed below.
Note that definitions of tangent vectors,
cotangent vectors and tensors in [Fr] use the
transformation rules in their definitions.
In [Lo] first the corresponding bundles are
constructed (mostly coordinate free), the
corresponding fields are defined as sections
and the transformation rules are a corollary.
In chapter 2 and later we also skip the discussion
on metric (g_ij), lowering and raising indices
and pseudo-forms.
Chapter 1
: all
Chapter 2 : all, except 2.1c, 2.1d, 2.3c
,2.3d, 2.4e, 2.7b, 2.8e
Chapter 3: Only 3.1, 3.2 and 3.3.
Chapter 4: Only 4.1, 4.2 until (4.25), 4.3a
Chapter 5: Only 5.1, 5.2 and 5.4 (treated
in some other way)
Handout :
De RhamCohomology
and section 13.4
Section 8.3 : Brouwer
degree + handout
PS . During my absense, you can contact Dr. Sergei Anisov
if necessary (Room 502 MI); email anisov@math.uu.nl.