$K$-Bad Spheres
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866912804413374464 |
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| author | Bendersky, Martin Thompson, Robert |
| author_facet | Bendersky, Martin Thompson, Robert |
| contents | In this paper we look at the $E$-completion of topological spaces where $E$ is a $p$-local ring spectrum. After a brief review of the concept of $E$-completion, we specialize to the case where $E=K$, $p$-local complex periodic $K$-theory, and consider the $K$-theory of the unstable sphere $S^{2n+1}$. We show that for certain values of $n$ and an odd prime $p$, the $K$-homology of the $K$-completion is not isomorphic to the $K$-homology of the sphere itself, thus in the terminology of Bousfield and Kan, these spheres are '$K$-bad'. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_02620 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | $K$-Bad Spheres Bendersky, Martin Thompson, Robert Algebraic Topology 55 (Primary) 55P60, 55N15 (Secondary) In this paper we look at the $E$-completion of topological spaces where $E$ is a $p$-local ring spectrum. After a brief review of the concept of $E$-completion, we specialize to the case where $E=K$, $p$-local complex periodic $K$-theory, and consider the $K$-theory of the unstable sphere $S^{2n+1}$. We show that for certain values of $n$ and an odd prime $p$, the $K$-homology of the $K$-completion is not isomorphic to the $K$-homology of the sphere itself, thus in the terminology of Bousfield and Kan, these spheres are '$K$-bad'. |
| title | $K$-Bad Spheres |
| topic | Algebraic Topology 55 (Primary) 55P60, 55N15 (Secondary) |
| url | https://arxiv.org/abs/2601.02620 |