University at Albany, College of Arts and Sciences

Department of Mathematics and Statistics

AMAT 540B: Topology II, Spring 2014


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


MWF 9:20–10:15 in ES-153.


AMAT 540A. (See the University‚Äôs Graduate Bulletin.)


From Wikipedia: Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism, though usually most classify up to homotopy equivalence. Although algebraic topology primarily uses algebra to study topological problems, using topology to solve algebraic problems is sometimes also possible. Algebraic topology, for example, allows for a convenient proof that any subgroup of a free group is again a free group.


None is required — but the following book, which is freely available online, is a recommended reference:


Weekly homework assignments, quizzes, midterm and final exams. The final exam is scheduled for Saturday, May 10, 3:30–5:30 in ES-153.

You are expected to attend all class meetings. The maximum number of absences permitted to receive credit for this course is 5 (five). Excessive tardiness may count as absence.

Of course, you are expected to 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.