University at Albany, College of Arts and Sciences

Department of Mathematics and Statistics

AMAT 840: Topics in Topology — Cohomology & Duality, Spring 2017


Prof. Marco Varisco,,
Office: ES-120C, Office Hours: TTh 11:35–12:30, or by appointment.


TTh 10:15–11:35 in ES-142.


AMAT 540 A & B, or permission of instructor.


The following topics will be covered, with many examples and applications throughout: singular cohomology groups, universal coefficient theorem, cup product, cohomology ring, Künneth theorem, Poicaré duality, de Rham theorem, relation to (stable) homotopy theory, cohomology operations, other cohomology theories.


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 — December 13, 2016.