Professor Francis Su
x73616, su @ math.hmc.edu
Office Hours: WED 1-2:30pm.
Course Content: This course is an introduction to algebraic and combinatorial topology, with an emphasis on simplicial and singular homology theory. A major theme in the course will be the connection between combinatorial and topological concepts. Topics will include simplicial complexes, simplicial and singular homology groups, exact sequences, chain maps, diagram chasing, Mayer-Vietoris sequences, Eilenberg-Steenrod axioms, Jordan curve theorem, and additional topics as time permits. This is standard first-year graduate material in pure mathematics.
Text: Munkres, Elements of Algebraic Topology. Doing the reading will be essential for success in this course.
Prerequisites: Analysis I (Math 131), Algebra I (Math 171), and Topology (Math 147, or topology summer readings), or the permission of the instructor. I will try to set up a few extra sessions to meet with those who did the summer readings.
A note about the course: Expect this course to be challenging, but also quite rewarding, as you see the interplay between algebra, topology, combinatorics, and analysis. I will run this course more like a graduate course. As such, I will expect a certain level of mathematical maturity. This means that sometimes I will not prove simple statements in class; you may have to work out some details for yourself or by doing the reading. My focus will be on proving the larger theorems and providing perspective on the material.
Homeworks: Homeworks, assigned weekly, turn in by Thursday 11am in bin outside my office door. Homeworks will be announced on the course webpage: http://www.math.hmc.edu/~su/math177a/
Honor Code: All are expected to abide by the HMC honor code. Cooperation is ENCOURAGED in this class, but write up all solutions individually and be sure to credit any collaborators.
| HW | Assignments | |
| HW #1 (due 9/13) |
"R" means read and think about the problem.
Only turn in problems NOT marked with an "R".
1 ( R1, 5 ), 2 ( 1, 3, 5, R6, R8, R10 ), 3 ( R1, 2, 4 ) In the last 2 problems, "describe" means: sketch the underlying space (if possible) and describe its topological type (if you can, e.g., is it homeomorphic to some familiar space)? |
Check solutions.
Available only within Claremont. |
| HW #2 (due 9/20) |
4 ( R1, 2, 3abc ), 5 ( 1, 2 ), and
Prove Lemma 5.3 (use the def'n of the boundary map; look at the book's proof only if you need a hint). |
Check solutions. |
| HW #3 (due 9/27) | 5 ( 4, 5 ), 6 ( 2, R4, 6, R7, 8 ) | Check solutions. |
| HW #4 (due 10/4) |
7 ( R1 ), 8 ( 1 ), 9 ( 2, 3 )
and READ Massey on the classification of surfaces. (Note that I sketched the solution to problem 9(3) in class except for the case i=1, which you are asked to do carefully here.) |
Check solutions. |
| week of 10/11 | Student Lectures | |
| week of 10/18 | Student Lectures | |
| week of 10/27 | no HW due to Fall Break | |
| HW #5 (due 11/1) |
12 ( 2 [in part (a), geometric descriptions of the maps suffice]),
23 ( 1 [statements (4) and (5) only], 3 ) 24 ( R1, R2, 3, 4 ) |
Check solutions. |
| HW #6 (due 11/8) | 24 ( 5 ) 25 ( 1, 4, 5 ) | Check solutions. |
| HW #7 (Sat. 11/17) | Attend the Mt. Baldy conference here at HMC, and write up summaries of the talks. | |
| HW #8 (due 11/29) |
DO these problems:
Problem A. Show that all universal objects in a category are equivalent. and DO 29 ( R1 ) 30 ( 2, R3 ) 33 ( 1, 4 ) |
Check solutions. |