Lecture Notes & Some Videos
Week 1: 1/10-1/14
From Munkres' Topology:
Section 58: notes video 1 video 2
Section 59: notes video
Section 60: notes video
Week 2: 1/17-1/21
MLK Day
Finitely Generated Abelian Groups (Roughly Sections 4 & 11)
Sections 1, 2, & 5 - Simplicial Complexes and Homology Groups Video 1 (19 min 43 sec) Video 2 (33 min 18 sec)
Example 1 Example 2 Example 3
Week 3: 1/24-1/28
Section 3 - Abstract Simplicial Complexes Video (6 min 48 sec)
Section 6 - Surfaces
Video 1 (23 min 11 sec)
Video 2 ( 9 min 29 sec) A little faint at first.
Video 3 (17 min 37 sec)
Week 4: 1/31-2/4
Section 7 - Dimension Zero and Reduced Homology Video (18 min 22 sec)
Section 8 - Cones Video (32 min 58 sec)
Week 5: 2/7-2/11
Section 9 - Relative Homology and Excision
Skip Section 10. (See bonus lectures at bottom of page.)
Section 12
Week 6: 2/14-2/18
Section 13
Chapter 2: 14-19
Skim Secion 20 on your own.
Week 7: 2/21-2/25
Section 21 Don't let this happen to you!
Section 22
Week 8: 2/28-3/4
Section 23 & 24 (Rough notes.)
Section 25
MV Examples
Exercise 6 on products of spheres
Example: Homology Groups of S2 x S3 x S7 x S7.
Week *: 3/7-3/11
SPRING BREAK!
Week 9: 3/14-3/18
Section 26: notes
Section 26, Braid Lemma and application: notes video (works best in Chrome) webm video format
Read over Sections 27 & 28 on your own.
Week 10: 3/21-3/25
Start Chapter 4.
Section 29, Part I: notes video
Section 29, Part II: notes video
Week 11: 3/28-4/1
Section 30, Part I: notes video
Section 30, Part II, Axiom 5: notes video a video b
Section 31, Axiom 6, Excision: notes video 1 video 2 video 3
Note: we skip Sections 32 & 33.
Week 12: 4/4-4/8
Section 34: notes video 1 video 2
Note: We skip Sections 35 & 36; skim Section 37 on your own.
The Hurewicz Homomorphism video 1 video 2
Section 38, CW Complexes. notes video
Week 13: 4/11-4/15
Section 39, Homology of CW Complexes.
notes 1 video 1
notes 2 video 2
notes 3 [Optional Reading]
Section 40, Projective Spaces. notes video
Seminar Talk on Lens Spaces
Week 14: 4/18-4/22
Start Chapter 5, Cohomology.
Section 41: The Hom Functor: notes video
Section 42: Simplicial Cohomology: notes 1 video 1
notes 2 video 2
Section 43: Relative Cohomology (skim)
Sections 44-6: Cohomology Theory (skim)
Section 47: notes video
Week 15: 4/25-4/29
Section 48: notes video
Section 49: notes video
example video 1 video 2
Section 73: notes video
See also: https://en.wikipedia.org/wiki/Solenoid_(mathematics)
Classification of Solenoids, by Aarts & Fokkink
Paper I wrote that uses Čech theory.
Week 16: 5/2-5/6
Final Exam Due 5/6.
Bonus Lectures!!
Section 50, Tensor Products of Abelian Groups: notes video
Section 10: notes video
Section 51: notes video