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This research aims to explore the classical topological invariants of homogeneous spaces using K-theory for simply connected compact simple Lie groups.

July 10, 2026Documenta MathematicaOpen Access

The classical topological invariants of homogeneous spaces

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Authors

JJJ. H. JonesExactech (United States)DRDmitriy RumyninUniversity of Warwick ATAdam R. ThomasUniversity of Warwick

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Investigates topological properties of homogeneous spaces formed by compact simple Lie groups, suggesting deeper connections in topology.

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This research aims to explore the classical topological invariants of homogeneous spaces using K-theory for simply connected compact simple Lie groups.
Analyzed homogeneous spaces G/K where G and K share the same rank.
Focused on examples from Cartan’s list of symmetric spaces, specifically EIII, EVI, and EVIII.
Applied general methods relevant for classical groups and exceptional groups.
Examined three symmetric spaces EIII, EVI, and EVIII, revealing their topological characteristics.
Identified the dimensions of these spaces as 32, 64, and 128, respectively.
Established that these spaces correspond to Rosenfeld projective planes.

Cite This Study

Jones et al. (2026) studied this question.

synapsesocial.com/papers/6a508afd6eeac72a4379fe04 https://doi.org/10.4171/dm/1085

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The classical topological invariants of homogeneous spaces

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The classical topological invariants of homogeneous spaces

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Cite This Study

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