The real Brown-Peterson homology of $Ω^ρS^{ρ+ 1}$
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912842471440384 |
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| author | Carrick, Christian Guillou, Bertrand Petersen, Sarah |
| author_facet | Carrick, Christian Guillou, Bertrand Petersen, Sarah |
| contents | We compute the $RO(C_2)$-graded real Brown--Peterson homology of the representation-loop space $Ω^ρS^{ρ+ 1}$, where $ρ$ is the regular representation of the cyclic group of order two. This calculation gives a $C_2$-equivariant analogue of the classical computation of Brown--Peterson homology of the double loop space $Ω^2 S^3$ due to Ravenel. Along the way, we develop comodule Nishida relations for $ρ$-loop spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_18019 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The real Brown-Peterson homology of $Ω^ρS^{ρ+ 1}$ Carrick, Christian Guillou, Bertrand Petersen, Sarah Algebraic Topology We compute the $RO(C_2)$-graded real Brown--Peterson homology of the representation-loop space $Ω^ρS^{ρ+ 1}$, where $ρ$ is the regular representation of the cyclic group of order two. This calculation gives a $C_2$-equivariant analogue of the classical computation of Brown--Peterson homology of the double loop space $Ω^2 S^3$ due to Ravenel. Along the way, we develop comodule Nishida relations for $ρ$-loop spaces. |
| title | The real Brown-Peterson homology of $Ω^ρS^{ρ+ 1}$ |
| topic | Algebraic Topology |
| url | https://arxiv.org/abs/2512.18019 |