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