MAT 542: Algebraic Topology II

Stony Brook University - Spring 2020

About the course

The course will cover homotopy groups, homotopy sequences of pairs and triples, locally trivial fibrations and Serre fibrations, the homotopy exact sequence of a Serre fibration, excision for homotopy groups, stable homotopy groups, extension problems, the obstruction cochain with values in homotopy groups of the fiber, for a crosssection, obstruction theory, Stiefel-Whitney and Euler classes of a vector bundle, Chern classes of a complex vector bundle.


basic point set topology, fundamental groups and covering spaces. A background in algebraic topology is not required, but certainly may be useful.


Oleg Viro
Professor, Ph.D. 1974, Doctor Phys-Mat.Sci. 1983,
both from Leningrad State University.
Arrived at Stony Brook in 2007.

Office: Math Tower 5-110
Phone: (631) 632-8286
Email: oleg.viro AT
Web page:

Research fields: Topology and Geometry,
especially low-dimensional topology
and real algebraic geometry.

Lectures time and location

Tuesdays and Thursdays 10:00am - 11:20pm in Zoom,
Meeting ID 445-647-2936
Required meeting password 237386

Online lectures


Office hours

Tuesdays and Thursdays 5:30pm - 7:00pm in Zoom,
Meeting ID 445-647-2936
Required meeting password 237386

or by appointment.


If you have a physical, psychological, medical, or learning disability that may impact your course work, please contact Disability Support Services or call (631) 632-6748. They will determine with you what accommodations are necessary and appropriate. All information and documentation is confidential. Students who require assistance during emergency evacuation are encouraged to discuss their needs with their professors and Disability Support Services. For procedures and information go to the Evacuation Guide for People with Physical Disabilities.

Academic Integrity

Each student must pursue his or her academic goals honestly and be personally accountable for all submitted work. Representing another person's work as your own is always wrong. Faculty are required to report any suspected instances of academic dishonesty to the Academic Judiciary. For more comprehensive information on academic integrity, including categories of academic dishonesty, please refer to the academic judiciary website.

Critical Incident Management

Stony Brook University expects students to respect the rights, privileges, and property of other people. Faculty are required to report to the Office of Judicial Affairs any disruptive behavior that interrupts their ability to teach, compromises the safety of the learning environment, or inhibits students' ability to learn.