Differential Topology
Math 7500, Winter 2012
Class:
- Math 7500
- 27 State Hall (note change)
- MWF 10:40 - 11:35
- Text:
Brocker and Janich, Introduction to Differential Topology
Here are my
notes from 1999.
The following texts will also be of interest.
-
Bjorn Ian Dundas,
Differential Topology
(available online)
-
John M. Lee,
Introduction to Smooth Manifolds
(very detailed with a lot of explanation)
-
John Milnor,
Topology from the Differentiable Viewpoint
(a classic gem)
-
Guillemin and Pollack,
Differential Topology
(a standard text)
-
Abraham, Marsden and Ratiu
Manifolds, Tensor Analysis and Applications
(aimed more at applications)
Professor:
Schedule:
You will
be responsible for material covered in class, whether it is in the book
or not. There will be tests.
Regular homework problems will be assigned and will be due at the start of
class on the assigned due date. Their role is to strengthen your grasp
on the material and fix it firmly in your memory.
Assignments:
(Text = Brocker and Janich's Introduction to Differential Topology.)
- Day 1
- Homework set 1 due Wednesday, 18 January.
Solutions
- Day 2 (pages 9 and up are repeated in Day 3 with improvements)
- Stereographic projection
- Projective space
- Day 3
- Note that Monday, 17 January, is Martin Luther King Day and there will be no class.
- Day 4
- Day 5
- Homework set 2 due Monday, 30 January.
Solutions
- Days 6 and 7
- Day 8
- Day 9 and
Addendum
- Day 10
- Homework set 3 due Friday, 10 February.
Solutions
- Day 11
- Day 12
- Day 13
- Homework set 4 due Wednesday, 22 February.
Solutions
- Day 14
- Day 15
- Day 16
- Day 17
- Day 18
- Day 19
- Homework set 5 due Monday, 5 March.
Hints
Solutions
- Day 20
- Day 21
- Day 22
- Day 23 (rough) (pp. 93-98)
- Homework set 6 due Monday, 19 March.
Solutions
- Day 24 (rough) (pp. 99-106)
- Day 25 (rough) (pp. 107-111)
- Day 26
- Day 27
- Homework set 7 due Friday, 30 March.
- Day 28
- Day 29
- Day 30
- Day 31
- Day 32
- Homework set 8 due Wednesday, 11 April.
- Day 33
- Day 34
- Day 35
- Day 36
- Day 37