Cobordism theory: Quillen's approach

Termine und Zeiten:

Vorlesungen: Freitag, 14-16 ct, Raum A 027.
Übungen: Montag, 12-14 ct, Raum B 039 (14-täglich ab 23.10).

Zusammenfassung:

In [1] Quillen proposed a new approach to the study of complex and unoriented cobordism, namely, he proposed to study these theories as universal theories on the category of smooth manifolds with a number of natural properties. This point of view also plays an important role in the theory of algebraic cobordism of Levine-Morel.

The present course will focus on the implementation of the program proposed by Quillen for unoriented cobordisms. In particular, we will leave the Pontrjagin-Thom theorem and the MO spectrum for another course, and instead talk about:
• Chern/Stiefel-Whitney classes;
• formal group laws;
• Steenrod operations;
• computation of the ring of unoriented cobordism;
• proof of the comparison theorem for unoriented cobordism and cohomology with coefficients in Z/2Z.

This course can also serve as an introduction to the theory of algebraic cobordism of Levine-Morel.

Voraussetzung:

This course will be of interest to Master students majoring in algebra or geometry. The course will be taught in English.

Klausur:

The exam will take place on Friday 16 February from 14:00 until 16:00 in room A027. No materials are permitted in the exam. Please ensure you bring with you an appropriate identity document with photo.
If you are considering taking the exam, please register by sending me a short email with your name and Matrikelnr.
Results of the exam
Solutions to the exam
Klausureinsicht will take place on Monday, February 19th from 12:00 until 14:00 in my office B427. Please write me an e-mail to confirm an appointment.

There are two opportunities to get ECTS points for the course.
1) Either you can get 3 ECTS points for attending my lectures and passing the exam.
2) Or you can get 6 ECTS points for attending my lectures and exercises, passing the exam, and also writing a 10-15 pages long exposition paper on a topic related to the topic of the course.
The exposition paper should be sent to me by email by no later than February 29.