# On the topology of the Rosenfeld Projective Planes

# On the topology of the Rosenfeld Projective Planes

**Online Talk**

**Zoom link: https://princeton.zoom.us/j/96282936122**

**Passcode: 998749**

The aim of this project is to study the topological invariants of the manifolds R_4, R_5, R_6, and R_7 of dimension 16, 32, 64, 128 which are known as the four exceptional Rosenfeld projective planes. These manifolds are homogeneous spaces for the exceptional Lie groups F_4, E_6, E_7, E_8 respectively.

The main idea is to exploit the fact that there are rather straightforward descriptions of the K-theory of Lie groups and homogeneous spaces in terms of representation theory. Since so much is known about the representation rings of the simply connected compact Lie groups, this gives a very efficient method of systematically calculating topological invariants of Lie groups and homogeneous spaces.

The talk will start with an introduction to the Rosenfeld projective planes and go on to explain how using ideas from K-theory really does help to understand them.

This is joint work with Dmitriy Rumynin and Adam Thomas who are both at Warwick.