University at Albany, College of Arts and Sciences

Department of Mathematics and Statistics

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

Instructor

Prof. Marco Varisco, [email protected], www.albany.edu/~mv312143/
Office: ES-120C, Office Hours: TTh 11:35–12:30, or by appointment.

Schedule

TTh 10:15–11:35 in ES-142.

Prerequisites

AMAT 540 A & B, or permission of instructor.

Description

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.

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 — December 13, 2016.