The $K$-Theory of the Sphere with the Antipodal Involution
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912649386655744 |
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| author | Boersema, Jeffrey L |
| author_facet | Boersema, Jeffrey L |
| contents | This is a thorough investigation on the real $K$-theory of the sphere $S^d$ associated with the antipodal involution. We calculate the algebraic structure of real $K$-theory and united $K$-theory for all $d$, we write down explicit unitaries representing the generators of all the non-trivial $K$-theory groups for $d \leq 4$, and we describe a recipe for generating such unitaries for all $d$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_16612 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The $K$-Theory of the Sphere with the Antipodal Involution Boersema, Jeffrey L K-Theory and Homology Operator Algebras 46L80 This is a thorough investigation on the real $K$-theory of the sphere $S^d$ associated with the antipodal involution. We calculate the algebraic structure of real $K$-theory and united $K$-theory for all $d$, we write down explicit unitaries representing the generators of all the non-trivial $K$-theory groups for $d \leq 4$, and we describe a recipe for generating such unitaries for all $d$. |
| title | The $K$-Theory of the Sphere with the Antipodal Involution |
| topic | K-Theory and Homology Operator Algebras 46L80 |
| url | https://arxiv.org/abs/2506.16612 |