A calibration in $\mathbf R^{16}$ and Federer's product question
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866916653696024576 |
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| author | Züst, Roger |
| author_facet | Züst, Roger |
| contents | Building upon the construction of a Cayley calibration adapted to a complex structure, we introduce a calibration $Φ$ in $\bigwedge^8 \mathbf R^{16}$ with $|Φ^2| = 294$. This enables us to show that the product of two orthogonally supported calibrations is not necessarily a calibration, thereby providing a negative answer to a question posed by Federer. Dadok and Harvey developed a general method for constructing calibrations as outer products of two unit spinors in the Clifford algebra. We show that $Φ$ arises from the product of two spinors with norm $1$ and $\sqrt{2}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_12402 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A calibration in $\mathbf R^{16}$ and Federer's product question Züst, Roger Differential Geometry Building upon the construction of a Cayley calibration adapted to a complex structure, we introduce a calibration $Φ$ in $\bigwedge^8 \mathbf R^{16}$ with $|Φ^2| = 294$. This enables us to show that the product of two orthogonally supported calibrations is not necessarily a calibration, thereby providing a negative answer to a question posed by Federer. Dadok and Harvey developed a general method for constructing calibrations as outer products of two unit spinors in the Clifford algebra. We show that $Φ$ arises from the product of two spinors with norm $1$ and $\sqrt{2}$. |
| title | A calibration in $\mathbf R^{16}$ and Federer's product question |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2503.12402 |