Math 527 - Spring 2019

Homotopy Theory

---

Instructor

Dominic Culver (dculver at illinois dot edu)
230 Illini
Office hours: M 4-5p

---

Time and Place

MWF 11-11:50 at 143 Altgeld Hall.

---

Course info

This class will be an introduction to stable homotopy theory. In particular, it will be an introduction to the stable homotopy category and we will study cohomology theories, such as topological K-theory, cobordism theories, and stable homotopy groups. We will also develop computational tools such as the Adams and Adams-Novikov spectral sequence. Along the way, we will study the algebra of cohomology operations (such as the Steenrod algebra), and see how these ideas can be used solve problems. Given time, we will study the Hopf invariant one problem, vector fields on spheres problem, and the calculation of the image of J.

---

Notes

What are spectra