Math 215A
Topology - Fall 2005
MWF 3:10 - 4:00, Wellman 125

Professor: Carol Gwosdz Gee
Office: Kerr Hall 687
Office Hours: W 1-2pm, Th 3-4pm, or by appointment
E-mail: cgee@math.ucdavis.edu
Textbook: Algebraic Topology, by Allen Hatcher.

Assignments:

# Due   Problems    (Please turn in starred problems.) Solutions
#1 F 10/7 pp. 18-19, #2*, 3, 5, 6a*, 6b*, 8, 10*, 13*, 14*, 17 2, 3, 5, 6a, 6b, 8, 10, 13, 14, 17
#2 F 10/14 pp. 18-19, #18*, 19, 20*, 21, 23*. 18, (or 18, or 18,) 19, 20, 21, 23,
#3 F 10/21 pp. 38-39, #1*, 2, 3*, 4, 5, 7* 1, 2, 3, 4, 5, 7
#4 F 10/28 pp. 38-39, #8, 9, 10*, 14, 15*, 16*, 19 8, 9, 10, 14, 15, 16 19     
#5 M 11/07 pp. 52-53, #2, 4*, 5, 7*, 8*, 12* (first part), 13 hint for 12, 2, 4, 5, 7, 8, 12, 12, 13
#6 M 11/14 Read pp. 47-52
p. 55 #19*, 21, 22
p. 79 #1, 2, 4*
ALSO TURN IN: Read the Torus Knots technique on p. 47 and determine the fundamental group of R^3 - K, where K is the right-handed trefoil knot, pictured (left) in the figure on that page. Then use the Wirtinger Presentation method in problem #22 to calculate the fundamental group of R^3 - K. Can you show that these two presentations represent the same group? There are other texts that discuss the Wirtinger Presentation (try Rolfsen's Knots and Links, for starters). 		19, 21, 22, 1, 2, 4, knots,
#7 M 11/21 p. 79 #6, 8, 10*, 11, 12* (pick one more to turn in, for a total of 3)
Also, find a covering space of X and a map f: Y --> X that doesn't lift. 		6, 10, 11, 12,
#8 F 12/2 p. 80 #13*, 14*, 18*, 21 (do first half - will finish next week) 13, 14, 18,
#9 F 12/9 p. 80 # 20*, 21*
TOPOLOGY FOOD DAY on Friday. Share your favorite topologically-interesting food!		 20, 21,
For #21, the cross-section of the universal cover is fixed now.

Announcements:

10/3 Supplement to M 10/3 class notes -- explicitly describe the homotopy equivalence between annulus and circle.
10/4 Thursday 10/6 office hours cancelled. Guest Lecturer (Duchin) on Friday.
10/18 The three posted solutions for HW2 #18 have very different approaches. All are valid and interesting.
11/1 Homework #5 will be due on MONDAY 11/07, not Friday 11/04.
I will hold extra office hours on Monday from 1-2pm.
11/1 Friday 11/11 is a holiday. No class.
11/8 Help me test my new form, and Leave me Feedback
11/21 Friday 11/25 is a holiday. No class. (There will be class on W 11/23)
11/21 Office hours will resume to the original Wed/Thurs schedule, except for Thanksgiving Day.
12/1 Office hours now held in new building, MSB 2113.
12/5 Course evaluations will be distributed on Wed. 12/7.
12/5 Bring your favorite topologically-cool food to share on Friday, 12/9.

Course Outline:

We will cover chapters 0 and 1 of Hatcher -- fundamental group and covering spaces. You can download and print these chapters for free off the author's website, http://www.math.cornell.edu/~hatcher/AT/ATpage.html, or the entire text can be purchased in paperback for about $33. Math 215B and 215C will also use Hatcher this year.

Grading:

Your grade will be based on problem sets (70%) and the final exam (30%). Your two lowest problem set scores will be dropped.

Problem Sets:

Problem sets will be collected weekly on Fridays, at the beginning of class. Late work will not be graded. You will be asked to turn in a subset of the assigned problems. Additionally, one student will be designated per problem to carefully write up a solution for the rest of the class. These individual write-ups will also count toward your homework score. Students are encouraged to discuss problems with each other; however, each student should write up solutions on their own. Please indicate the names of other students who collaborated with you on each problem.