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• W3044007410 abstract "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 $$mathbb {R}_{ge 0}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msub> <mml:mi>R</mml:mi> <mml:mrow> <mml:mo>≥</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:msub> </mml:math> . 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 $$l^1$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msup> <mml:mi>l</mml:mi> <mml:mn>1</mml:mn> </mml:msup> </mml:math> -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." @default.
• W3044007410 created "2020-07-29" @default.
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• W3044007410 date "2020-07-24" @default.
• W3044007410 modified "2023-10-11" @default.
• W3044007410 title "The spectrum of simplicial volume" @default.
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• W3044007410 doi "https://doi.org/10.1007/s00222-020-00989-0" @default.
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