University at Albany, College of Arts and Sciences

Department of Mathematics and Statistics

AMAT 840: Topics in Topology — Homotopy Theory, Fall 2011


Prof. Marco Varisco,,
Office: ES-120C, Office Hours: M 2:45–5:35, W 2:45–4:05, or by appointment.


MWF 1:40–2:35 in ES-146.


AMAT 540 A & B.


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, are both excellent references:


Biweekly homework assignments.

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 31, 2011.