Instructor
Prof. Marco Varisco,
[email protected],
www.albany.edu/~mv312143/
Office: ES-120C,
Office Hours: MWF 10:25–11:20, or by appointment.
Schedule
MWF 11:30–12:25 in ES-143.
Prerequisites
AMAT 540 A & B, or permission of instructor.
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 and can be purchased for less than $30 each, 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
Weekly homework assignments.
Late submissions will not be accepted. Regular attendance is expected, and excessive tardiness may count as absence. We refer to the Graduate Bulletin for the policies on incomplete grades. Of course, students must follow the University’s Standards of Academic Integrity.