Math 215a: Algebraic topology
UC Berkeley, Fall 2003
Instructor
Michael
Hutchings
hutching@math.berkeley.edu
Office phone: 510-642-4329.
Office: 923 Evans.
Tentative office hours: Tuesday 3 - 5
(primarily for Math 53), Thursday 10-11 (primarily for Math 215a).
About the course
Algebraic topology is a beautiful subject developing algebraic
invariants (homology, homotopy groups, etc.) which extract the
"essence" of a topological space and provide powerful machinery for
proving many deep theorems (Brouwer fixed point theorem, Jordan curve
theorem, many others like this, classification results, etc.).
In the first semester we will begin to study the essential "core"
material of algebraic topology: homotopy groups, homology, and
cohomology, and interesting examples and applications thereof.
In the second semester we will finish whatever is left over from the
first semester, and then study a selection of more advanced, but still
very important topics. Possible topics include but are not limited to
bundles and characteristic classes, Morse theory, and spectral
sequences.
Textbook
The textbook for the core material that we will be doing in the first
semester and some of the second semester is "Algebraic topology" by
Allen Hatcher; this is available in paperback from Cambridge
University Press, and can also be downloaded from the author's
website, although printing out the whole book might cost more than
buying it. A little bit in the first semester, and a lot in the
second semester, we will discuss some topics and perspectives that
are not in this book. I will post additional references here later.
Prerequisites
Basic knowledge of abstract algebra, linear algebra, and point-set
topology, together with sufficient independence and mathematical
maturity to handle a graduate course, are essential. Undergraduate
algebraic or differential topology would be helpful but is not required.
Lecture summaries and plans