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arXiv · 2503.12402

A calibration on $\mathbf R^{16}$ and Federer's product question

Roger Züst
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Abstract

Building upon the construction of a Cayley calibration adapted to a complex structure, we introduce a calibration $\Phi$ in $\bigwedge^8 \mathbf R^{16}$ with $|\Phi^2| = 294$. 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 $\Phi$ arises from the product of two spinors with norm $1$ and $\sqrt{2}$.

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Roger Züst. 2025-03-16. A calibration on $\mathbf R^{16}$ and Federer's product question. https://arxiv.org/abs/2503.12402

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