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The spectrum of simplicial volume

Accepted version
Peer-reviewed

Type

Article

Change log

Authors

Löh, C 

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 R≥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 l1-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.

Description

Keywords

math.GT, math.GT, 57N65, 57M07, 20J05

Journal Title

Inventiones Mathematicae

Conference Name

Journal ISSN

0020-9910
1432-1297

Volume Title

223

Publisher

Springer Science and Business Media LLC

Rights

All rights reserved