University at Albany, College of Arts and Sciences

Department of Mathematics and Statistics

AMAT 840: Topics in Topology — Homotopy Theory, Fall 2016


Prof. Marco Varisco,,
Office: ES-120C, Office Hours: MWF 10:25–11:20, or by appointment.


MWF 11:30–12:25 in ES-143.


AMAT 540 A & B, or permission of instructor.


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.


None—but the following books, which are freely available online and can be purchased for less than $30 each, are both excellent references:


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.

This syllabus is subject to change. All official announcements and assignments are given in class, and this web page may not be up to date.
Marco Varisco — August 1, 2016.