Heuer, Nicolaus ; Löh, Clara
Alternative Links zum Volltext:DOIVerlag
| Dokumentenart: | Artikel |
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| Titel eines Journals oder einer Zeitschrift: | Inventiones mathematicae |
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| Verlag: | SPRINGER HEIDELBERG |
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| Ort der Veröffentlichung: | HEIDELBERG |
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| Band: | 223 |
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| Nummer des Zeitschriftenheftes oder des Kapitels: | 1 |
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| Seitenbereich: | S. 103-148 |
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| Datum: | 2021 |
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| Institutionen: | Mathematik > Prof. Dr. Clara Löh |
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| Identifikationsnummer: | | Wert | Typ |
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| 10.1007/s00222-020-00989-0 | DOI |
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| Stichwörter / Keywords: | STABLE COMMUTATOR LENGTH; MAPPING CLASS-GROUPS; BOUNDED COHOMOLOGY; GROMOV INVARIANT; FREE-PRODUCTS; SCL; SUBGROUPS; HOMOLOGY; GENUS; |
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| Dewey-Dezimal-Klassifikation: | 500 Naturwissenschaften und Mathematik > 510 Mathematik |
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| Status: | Veröffentlicht |
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| Begutachtet: | Ja, diese Version wurde begutachtet |
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| An der Universität Regensburg entstanden: | Ja |
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| Dokumenten-ID: | 55644 |
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Zusammenfassung
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. ...
Zusammenfassung
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.
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