University at Albany, College of Arts and Sciences

Department of Mathematics and Statistics

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

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:

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.


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.