The classical topological invariants of homogeneous spaces
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866910191075721216 |
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| author | Jones, John Rumynin, Dmitriy Thomas, Adam R. |
| author_facet | Jones, John Rumynin, Dmitriy Thomas, Adam R. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_14365 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The classical topological invariants of homogeneous spaces Jones, John Rumynin, Dmitriy Thomas, Adam R. Algebraic Topology Geometric Topology Representation Theory 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. |
| title | The classical topological invariants of homogeneous spaces |
| topic | Algebraic Topology Geometric Topology Representation Theory |
| url | https://arxiv.org/abs/2310.14365 |