The classical topological invariants of homogeneous spaces

John Jones; Dmitriy Rumynin; Adam R. Thomas

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arXiv · 2310.14365

The classical topological invariants of homogeneous spaces

John Jones·Dmitriy Rumynin·Adam R. Thomas

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Abstract

We study the homogeneous spaces of a simply connected, compact, simple Lie group $G$ through the lens of K-theory. Our methods apply equally well to the case where $G$ is in one of the four infinite families of classical groups, or one of the five exceptional groups. The main examples we study in detail are the four symmetric spaces FII, EIII, EVI, EVIII in Cartan's list of symmetric spaces. These are, respectively, homogeneous spaces for $F_4$, $E_6$, $E_7$, $E_8$ with dimensions $16$, $32$, $64$, $128$. They are the four Rosenfeld projective planes.

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BibTeX RIS

John Jones, Dmitriy Rumynin, Adam R. Thomas. 2023-10-22. The classical topological invariants of homogeneous spaces. https://arxiv.org/abs/2310.14365

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