| Date |
Topics |
Book |
Event |
| Week 1 |
| Jan 09 |
|
|
Homework 1 posted. |
| Jan 10 |
What is homotopy? The fundamental group. |
Pages 1-14, Section 1.1 |
Handout given. |
| Jan 11 |
|
|
|
| Jan 12 |
Basepoints and the fundamental group of the circle. Functoriality. |
Section 1.1 |
|
| Jan 13 |
|
|
|
| Week 2 |
| Jan 16 |
|
|
Martin Luther King Jr. Day |
| Jan 17 |
Fundamental group of spheres. Van Kampen's theorem. |
Sections 1.1, 1.2 |
|
| Jan 18 |
|
|
Homework 2 posted. |
| Jan 19 |
The fundamental group of CW-complexes. |
Sections 1.2, 1.A, 0 |
Homework 1 due by 5pm. |
| Jan 20 |
|
|
Solutions to homework 1
posted. Correction about subtrees of graphs. |
| Week 3 |
| Jan 23 |
|
|
|
| Jan 24 |
Covering spaces. Lifting properties. |
Section 1.3 |
|
| Jan 25 |
|
|
Homework 3 posted. |
| Jan 26 |
Covering spaces and the fundamental group. |
Section 1.3 |
|
| Jan 27 |
|
|
Homework 2 due by 5pm. Final day to add or drop a class (5pm). Solutions to homework 2
posted. |
| Week 4 |
| Jan 30 |
|
|
|
| Jan 31 |
The correspondence theorem. |
Sections 1.3 |
Homework 3 due date changed to February 7th. |
| Feb 01 |
|
|
|
| Feb 02 |
Group actions. Singular homology. |
Sections 1.3, 1.A, 2.1 |
|
| Feb 03 |
|
|
|
| Week 5 |
| Feb 06 |
|
|
|
| Feb 07 |
Singular homology, path components and the fundamental group. |
Section 2.1, 2.A |
Homework 3 due by 5pm. Midterm exam posted. |
| Feb 08 |
|
|
Solutions to homework 3 posted. |
| Feb 09 |
Homotopy invariance of singular homology. Long exact sequence of a pair. |
Sections 2.1, 2.2 |
|
| Feb 10 |
|
|
|
| Week 6 |
| Feb 13 |
|
|
Rewriting of the proof of homotopy invariance of singular
homology from the textbook. |
| Feb 14 |
The homology of the spheres and the Mayer-Vietoris sequence. |
Sections 2.1, 2.2 |
|
| Feb 15 |
|
|
|
| Feb 16 |
Cellular homology and degree of maps. |
Sections 2.1, 2.2 |
Midterm due by 5pm. Homework 4 posted. |
| Feb 17 |
|
|
Solutions to Midterm posted. |
| Week 7 |
| Feb 20 |
|
|
Presidents' day |
| Feb 21 |
Cellular homology and degree of maps II. |
Sections 2.2 |
|
| Feb 22 |
|
|
|
| Feb 23 |
Classical applications of homology. |
Section 2.B |
|
| Feb 24 |
|
|
|
| Week 8 |
| Feb 27 |
|
|
Homework 5 posted. |
| Feb 28 |
The proof of excision. The homology of projective spaces. |
Sections 2.1, 2.2 |
Homework 4 due by 5pm. Solutions to homework 4 posted. |
| Feb 29 |
|
|
|
| Mar 01 |
Singular cohomology. The universal coefficient theorem for cohomology. |
Sections 3.1 |
|
| Mar 02 |
|
|
Deadline for withdrawing and change of grading basis (5pm). |
| Week 9 |
| Mar 05 |
|
|
Homework 6 posted. |
| Mar 06 |
The cup product and the cohomology ring. |
Section 3.2 |
Homework 5 due by 5pm. Solutions to homework 5 posted. |
| Mar 07 |
|
|
|
| Mar 08 |
Kunneth formula and the cohomology ring of projective spaces. |
Section 3.2 |
|
| Mar 09 |
|
|
|
| Week 10 |
| Mar 12 |
|
|
|
| Mar 13 |
Orientability and homology with coefficients. |
Sections 2.2, 3.3 |
|
| Mar 14 |
|
|
|
| Mar 15 |
Poincare duality. |
Section 3.3 |
Homework 6 due by 5pm. Solutions to homework 6 posted. |
| Mar 16 |
|
|
|
| Final Exam |
| Mar 22 |
|
|
Final Exam, 3:30-6:30pm, Room 380-380F. Solutions to final exam posted. |
| Mar 26 |
|
|
Exams section updated and final grades submitted. |