Instructor
Prof. Marco Varisco,
[email protected],
www.albany.edu/~mv312143/
Office: ES-120C,
Office Hours: M 2:45–5:35, W 2:45–4:05, or by appointment.
Schedule
MWF 1:40–2:35 in ES-146.
Prerequisites
AMAT 540 A & B.
Description
The topic of the course will be classical homotopy theory, presented from a modern point of view: homotopy groups of spaces, their fundamental properties, the long exact sequence of a fibration, the theorems of Whitehead and Hurewicz, Blakers-Massey homotopy excision theorem and its applications (in particular Freudenthal suspension theorem), the relation with (co)homology theories, and a glimpse of stable homotopy theory.
Textbooks
None, but the following books, which are freely available online, are both excellent references:
- Allen Hatcher, Algebraic Topology,
Cambridge University Press, 2002.
math.cornell.edu/~hatcher/AT/ATpage.html -
J. Peter May, A Concise Course in Algebraic Topology,
The University of Chicago Press, 1999.
math.uchicago.edu/~may/BOOKSMaster.html
Grading
Biweekly homework assignments.