Math 205C, Topology

Spring 2015

MWF 12:10-1 pm,
Surge 268

Monday, March 30: Topological manifolds

Wednesday, April 1: Smooth structures

Exercises:
1-2, 1-4, and 1.18 (due Wednesday, April 8)

Friday, April 3: Class cancelled

Monday, April 6: Examples of smooth manifolds

Exercises:
1.20 (due Wednesday, April 8)

Wednesday, April 8: Manifolds with boundary

Exercises: Use
lemma to get smooth structure on S^{2}, 1.39, 1.44 (due Wednesday,
April 15)

Friday, April 10: Smooth maps

Exercises:
1-12 and 2.7 (due Wednesday, April 15)

Monday, April 13: Diffeomorphisms of smooth manifolds

Exercise: 2.19
(due Wednesday, April 22)

Wednesday, April 15: Partitions of unity

Exercise: 2.27
(due Wednesday, April 22)

Friday, April 17: Tangent spaces in Euclidean space

Exercise: 2-10
(due Wednesday, April 22)

Monday, April 20: Tangent spaces and differentials

Exercise: 3.7
(due Friday, May 1)

Wednesday, April 22: Tangent spaces and coordinates

Exercise: 3-2
(due Friday, May 1)

Friday, April 24: Tangent bundles

Monday, April 27: Local diffeomorphisms and the Inverse Function
Theorem

Exercises: 3-3
(due Friday, May 1); 4.4 and 4.10 (no boundary case) (due Wednesday, May 6)

Wednesday, April 29: The Rank Theorem

Friday, May 1: Smooth embeddings

Exercise: 4-2
(due Wednesday, May 6)

Monday, May 4: Smooth submersions

Exercise: 4.34
(due Wednesday, May 6)

Wednesday, May 6: Embedded submanifolds

Friday, May 8: Level sets

Exercises:
5-1, 5-2, and 5-3 (due Wednesday, May 13)

Monday, May 11: Immersed submanifolds and
tangent spaces to submanifolds

Wednesday, May 13: Sard’s theorem and embeddings into Euclidean space

Friday, May 15: Midterm exam

Monday, May 18: Whitney Embedding Theorem

Exercise: 6-2
(due Wednesday, May 27)

Wednesday, May 20: Tubular neighborhoods

Friday, May 22: Whitney approximation

Exercise: 6-8
(due Wednesday, May 27)

Monday, May 25: Memorial Day – no class

Wednesday, May 27: Transversality

Exercises:
6-10 and 6-13 (due Wednesday, June 3)

Friday, May 29: Lie groups

Exercise: 7-7
(due Wednesday, June 3)

Monday, June 1: Vector fields

Exercise: 8-1
(due Wednesday, June 3)

Wednesday, June 3: Frames and vector fields as derivations

Friday, June 5: Lie brackets and Lie algebras

Monday, June 8: Final Exam 7-10 pm

Last updated: 5 June 2015