The Atiyah-Sutcliffe conjecture and $E_n$-algebras
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866915005413195776 |
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| author | Guerra, Lorenzo Salvatore, Paolo |
| author_facet | Guerra, Lorenzo Salvatore, Paolo |
| contents | We show that a certain conjecture by Atiyah and Sutcliffe implies the existence of an $ E_3 $-algebra (respectively $ E_2 $-algebra) structure on the disjoint union of all complex (respectively real) full flag manifolds modulo symmetric groups. Moreover, we show that these structures are liftings of exotic $ E_3 $ (respectively $ E_2 $) structures on the free $ E_\infty $-algebras on $ BU(1)+ $ (respectively $ BO(1)+ $), that do not extend to $ E_4 $ (respectively $ E_3 $) structures. We also provide some (co)homological calculations supporting the conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_24124 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Atiyah-Sutcliffe conjecture and $E_n$-algebras Guerra, Lorenzo Salvatore, Paolo Algebraic Topology 55R80, 55S12, 55P48, 55S15 We show that a certain conjecture by Atiyah and Sutcliffe implies the existence of an $ E_3 $-algebra (respectively $ E_2 $-algebra) structure on the disjoint union of all complex (respectively real) full flag manifolds modulo symmetric groups. Moreover, we show that these structures are liftings of exotic $ E_3 $ (respectively $ E_2 $) structures on the free $ E_\infty $-algebras on $ BU(1)+ $ (respectively $ BO(1)+ $), that do not extend to $ E_4 $ (respectively $ E_3 $) structures. We also provide some (co)homological calculations supporting the conjecture. |
| title | The Atiyah-Sutcliffe conjecture and $E_n$-algebras |
| topic | Algebraic Topology 55R80, 55S12, 55P48, 55S15 |
| url | https://arxiv.org/abs/2410.24124 |