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On the topology of the Rosenfeld Projective Planes

Algebraic Topology Seminar

On the topology of the Rosenfeld Projective Planes

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John Jones, University of Warwick

Online Talk

Zoom link:Ìý

Passcode: 998749

The aim of this project is to study the topological invariants of the manifoldsÌýR_4, R_5, R_6, and R_7 of dimension 16, 32, 64, 128Ìý which are known asÌýthe four exceptional Rosenfeld projective planes.Ìý 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 homogeneousÌýspaces in terms of representation theory.ÌýSince so much is known about theÌýrepresentation rings of the simplyÌýconnected compact Lie groups, this gives a very efficient method of systematically calculatingÌýtopological invariants of Lie groups and homogeneous spaces.

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

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