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

Instructor

Prof. Marco Varisco, mvarisco@albany.edu, 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.