Math 7512, Topology II
MWF 11:40-12:30
112 Lockett
Spring 2008
· Professor: Tara E. Brendle
· Office: Lockett 254
· Office Hours: MF 10:30-11:30am (Please note: I am NOT in my office on Wednesdays at this time due to committee meetings!)
· E-mail: brendle@math.lsu.edu
· Phone: 578-1657
Prerequisite: Math 7510 or equivalent
Course Description: This course will essentially cover the
basics of homology and cohomology theory. We will begin with a brief treatment of
covering spaces (we will briefly review the material on covering spaces already
seen in Math 7510 and also discuss covering space automorphisms). We will then move on to simplicial and singular homology as well as fundamental
computational techniques such as the Mayer-Vietoris
sequence. We will then learn
aspects of cohomology theory, including the Universal
Coefficient Theorem, cup products, the Kunneth
Formula, and Poincare Duality. If
time permits we will also cover topics such as the Hurewicz
Theorem and elementary category theory.
Text: Allen Hatcher, Algebraic Topology. This is published by Cambridge
University Press, but it is also available for free on Allen Hatcher's webpage (along
with several other useful sets of notes on various other topics in
topology).
Additional Resources: W. S. Massey’s two texts, “Algebraic Topology: An Introduction” and “A Basic Course in Algebraic Topology” are good references; in particular, I will be following Massey’s treatment of covering transformations to a certain extent. As the semester progresses, I will be listing here other texts and papers which you may find useful as supplementary material.
Homework: Homework problems will be assigned and collected regularly
in class throughout the semester.
The purpose of these exercises is to help the student engage with the
material and to practice the techniques and concepts learned in the
course. Click HERE for a
list of problems and due dates.
Quizzes: We will regularly have brief in-class
quizzes testing you on various terms and examples we have learned in
class. These quizzes will always be
announced in advance. Click HERE for a
list of dates and the corresponding lists of which terms/examples you’re
responsible for.
Assessment: Homeworks will
count for 50% of your grade.
In-class “definition/example quizzes” will count for 25% of
your grade. There will be a final
exam which will count for 25% of your grade and which will serve as a model for
the Core II exam to be given later in the year. The final exam is scheduled for Tuesday,
May 6, 2008, from 10am-noon. Solutions to the
final can be found HERE.