The spectrum of simplicial volume

• 成果类型: Article
• 署名作者: Heuer, Nicolaus; Loeh, Clara
• 署名单位: University of Cambridge; University of Regensburg
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-020-00989-0
• 发表日期: 2021
• 页码: 103-148
• 关键词: stable commutator length; mapping class-groups; bounded cohomology; gromov invariant; free-products; scl; SUBGROUPS; HOMOLOGY; genus

摘要

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 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.