University at Albany, College of Arts and Sciences

Department of Mathematics & Statistics

AMAT 840: Topics in Topology — Cohomology & Duality, Fall 2021

Instructor

Prof. Marco Varisco, [email protected], albany.edu/~mv312143
Office: ES-120B, Office Hours: by appointment.

Schedule

TuTh 1:30–2:50 in ES-153.

Prerequisites

AMAT 540 A & B, or permission of instructor.

Description

This course could be called AMAT 540 C, since it’s an ideal follow-up to 540 B. We will learn the following topics, with many examples and applications throughout: cohomology groups, universal coefficient theorem, cup products, cohomology rings, Künneth theorem, and Poicaré duality. Depending on the participants’ interests, we will also explore some of the following additional topics: de Rham theorem, relation to stable homotopy theory, cohomology operations, and other cohomology theories.

Textbooks

None will be followed closely—but the following two books, which are both freely available online and can be purchased for about $30 each, are excellent references:

Grading

Homework assignments.


New York State Education Law (Section 224-A) requires campuses to excuse, without penalty, individual students absent because of religious beliefs, and to provide equivalent opportunities for make-up examinations, study, or work requirements missed because of such absences. I will work directly with you to accommodate religious observances, provided that you notify me in a timely manner.

Reasonable accommodations will be provided for students with documented physical, sensory, systemic, medical, cognitive, learning, and mental health (psychiatric) disabilities. If you believe you have a disability requiring accommodation in this class, please notify the Disability Access and Inclusion Student Services ([email protected]). Upon verification and after the registration process is complete, the DAISS will provide you with a letter that informs me that you are a student with a disability registered with the DAISS and lists the recommended reasonable accommodations.

Of course, you are expected to follow the University’s Standards of Academic Integrity and Medical Excuse Policies. We refer to the Graduate Bulletin for the policies on incomplete grades.


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.