The spectrum of simplicial volume

Nicolaus Heuer; Clara Loeh

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arXiv · 1904.04539

The spectrum of simplicial volume

Nicolaus Heuer·Clara Loeh

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Abstract

New constructions in group homology allow us to manufacture high-dimensional manifolds with controlled simplicial volume. We prove that for every dimension bigger than 3 the set of simplicial volumes of orientable closed connected manifolds is dense in $\mathbb{R}_{\geq 0}$. In dimension 4 we prove that every non-negative rational number is the simplicial volume of some orientable closed connected 4-manifold. Our group theoretic results relate stable commutator length to the $l^1$-semi-norm of certain singular homology classes in degree 2. The output of these results is translated into manifold constructions using cross-products and Thom realisation.

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Nicolaus Heuer, Clara Loeh. 2019-04-09. The spectrum of simplicial volume. https://arxiv.org/abs/1904.04539

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