A stable splitting for spaces of commuting elements in unitary groups
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916586076504064 |
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| author | Adem, Alejandro Gómez, José Manuel Gritschacher, Simon |
| author_facet | Adem, Alejandro Gómez, José Manuel Gritschacher, Simon |
| contents | We prove an analogue of Miller's stable splitting of the unitary group $U(m)$ for spaces of commuting elements in $U(m)$. After inverting $m!$, the space $\text{Hom}(\mathbb{Z}^n,U(m))$ splits stably as a wedge of Thom-like spaces of bundles of commuting varieties over certain partial flag manifolds. Using Steenrod operations we prove that our splitting does not hold integrally. Analogous decompositions for symplectic and orthogonal groups as well as homological results for the one-point compactification of the commuting variety in a Lie algebra are also provided. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_09229 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A stable splitting for spaces of commuting elements in unitary groups Adem, Alejandro Gómez, José Manuel Gritschacher, Simon Algebraic Topology We prove an analogue of Miller's stable splitting of the unitary group $U(m)$ for spaces of commuting elements in $U(m)$. After inverting $m!$, the space $\text{Hom}(\mathbb{Z}^n,U(m))$ splits stably as a wedge of Thom-like spaces of bundles of commuting varieties over certain partial flag manifolds. Using Steenrod operations we prove that our splitting does not hold integrally. Analogous decompositions for symplectic and orthogonal groups as well as homological results for the one-point compactification of the commuting variety in a Lie algebra are also provided. |
| title | A stable splitting for spaces of commuting elements in unitary groups |
| topic | Algebraic Topology |
| url | https://arxiv.org/abs/2404.09229 |