Heuer, Nicolaus and Loeh, Clara (2021) The spectrum of simplicial volume. INVENTIONES MATHEMATICAE, 223 (1). pp. 103-148. ISSN 0020-9910, 1432-1297
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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.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | STABLE COMMUTATOR LENGTH; MAPPING CLASS-GROUPS; BOUNDED COHOMOLOGY; GROMOV INVARIANT; FREE-PRODUCTS; SCL; SUBGROUPS; HOMOLOGY; GENUS; |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Clara Löh |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 18 Jan 2022 07:27 |
| Last Modified: | 18 Jan 2022 07:27 |
| URI: | https://pred.uni-regensburg.de/id/eprint/44167 |
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