On the stable norm of slit tori and the Farey sequence

Pablo Montealegre

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arXiv · 2310.05570

On the stable norm of slit tori and the Farey sequence

Pablo Montealegre

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Abstract

Let (M, g) be a compact manifold endowed with a possibly singular Riemannian metric. The metric induces a norm on the homology of M , called the stable norm. We provide explicit computations of the stable norm of flat slit tori using the Farey sequence. We then glue several slit tori together to produce half-translation surfaces whose unit ball of the stable norm has faces of maximal dimension. Furthermore, we give a sub-quadratic estimate for the asymptotic counting of simple homology classes on these surfaces.

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Pablo Montealegre. 2023-10-09. On the stable norm of slit tori and the Farey sequence. https://arxiv.org/abs/2310.05570

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