A note on common complements
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910764776816640 |
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| author | Andruchow, Esteban Chiumiento, Eduardo |
| author_facet | Andruchow, Esteban Chiumiento, Eduardo |
| contents | We discuss the structure of the set $Δ$ consisting of pairs of closed subspaces that have a common complement in a Hilbert space previously studied by Lauzon and Treil (J. Funct. Anal. 212: 500--512, 2004). We prove that $Δ$ is the base space of a real analytic fiber bundle constructed in terms of geometric objects associated to the Grassmann manifold. As a consequence we determine the homotopy type of $Δ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_19316 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A note on common complements Andruchow, Esteban Chiumiento, Eduardo Functional Analysis General Topology 47B02, 57N20, 58B10 47B02, 57N20, 58B10 47B02, 57N20, 58B10 We discuss the structure of the set $Δ$ consisting of pairs of closed subspaces that have a common complement in a Hilbert space previously studied by Lauzon and Treil (J. Funct. Anal. 212: 500--512, 2004). We prove that $Δ$ is the base space of a real analytic fiber bundle constructed in terms of geometric objects associated to the Grassmann manifold. As a consequence we determine the homotopy type of $Δ$. |
| title | A note on common complements |
| topic | Functional Analysis General Topology 47B02, 57N20, 58B10 47B02, 57N20, 58B10 47B02, 57N20, 58B10 |
| url | https://arxiv.org/abs/2412.19316 |