Instructor: Mike Sullivan
Office: LGRT 1544 Phone: 545-1909
email: my last name <at> math <at> umass
<at> edu
Office hours: Monday 3:45-5:25 on weeks when HW is due.
Or by appointment on Monday before noon or Wednesday before 11:30 any week.
Text
Required: Algebraic Topology , by Allen Hatcher. It costs about
$22-$35 on Amazon.com, for example.
This text can also be legally downloaded for free at
Hatcher's website.
Recommended: Geometry and Topology , by Glen Bredon. It costs
about $37-$75 at Amazon.com, for example. The text is also on reserve
at the library.
Description:
This course will be centered on Chapters 1 (fundamental group),
2 (homology) and 3 (cohomology) of the Hatcher text.
Ideally, if time permits, there will be some topics/examples on
differential topology coming from the Bredon text.
The grade will be based on the timely completion of several
homeworks.
Prerequisites are Math 671 which is point set topology,
and a few definitions from algebra like groups, rings, and homomorphisms.
Announcements:
05/05: HW 5 due date has been pushed back two days to Friday May 16, 2pm.
03/24: We will not meet on Monday May 11. Instead there will be a make-up
class on Monday Arpil 7, 3:50-5:05 (immediately following the regular
class).
02/25: By popular demand, HW 2 is now due on Monday 3/3
02/11: By popular demand, HW 1 is now due on Tuesday 2/19 (which
is a ``Monday").
02/05: I just realized I have a job talk to attend at 4-5pm
on Monday 02/11, so those office hours will be rescheduled to 10:45-11:45am
and 5:00-5:25pm, same day.
01/30: Check out the links to
covering spaces of S^1 and
the fundamental group of T^2. (Thanks Aaron)
Homework
HW 1: Due Weds 2/13 in class. NOW DUE TUES 2/19 in class.
#3, 6, 16 in Section 1.1 (of Hatcher, unless otherwise indicated)
#7, 10, 17 in Section 1.2
HW 2: Due Weds 2/27 in class.
#4, 12, 14, 18, 27 in Section 1.3
Prove that the fundamental group of a topological group,
with base point the identity element, is abelian.
HW 3: Either the first five problems by Weds 3/5, or all 6 problems
by Weds 3/19.
#8, 12, 14 (last question only), 17b (compute H_n(X,A) only), 18, 27
in Section 2.1.
Hint for 17b: the inclusion i:A ->X induces the zero map i_*:H_1(A) -> H_1(X).
HW 4: Either the first five problems (3 from Hatcher + first two from class)
by Weds 4/9, or all 6 problems by Weds 4/16.
#2, 8, 17 in Section 2.2
The three problems written down in class on Weds 3/26.
HW 5: Due May 16 by 2pm. If you turn it in at the last class on May 7
you do not need to do Section 3.3 # 5 and the last in-class problem.
This is the last homework and will be weighted
as 1.5 HWs
#20, 22 in Section 2.2
#5 in Section 2.C
#1, 11 in Section 3.2
#5 in Section 3.3
The 3 problems written down in class on Weds 4/16.