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Positive simplicial
volume implies virtually positive Seifert volume for
$3$–manifolds
Pierre Derbez, Yi Liu, Hongbin Sun and Shicheng Wang |
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Geometry & Topology 21 (2017) 3159–3190
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Abstract |
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We show that for any closed orientable –manifold with positive simplicial volume, the growth of the Seifert volume of its finite covers is faster than the linear rate. In particular, each closed orientable –manifold with positive simplicial volume has virtually positive Seifert volume. The result reveals certain fundamental differences between the representation volumes of hyperbolic type and Seifert type. The proof is based on developments and interactions of recent results on virtual domination and on virtual representation volumes of –manifolds. |
Keywords
Seifert volume, nonzero degree maps, growth rate
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Mathematical Subject Classification 2010
Primary: 57M50
Secondary: 51H20
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References |
Publication
Received: 6 July 2016
Accepted: 23 December 2016
Published: 15 August 2017
Proposed: Cameron Gordon
Seconded: Gang Tian, Walter Neumann
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Authors |
| Pierre Derbez | |
| Aix Marseille Université CNRS UMR 7373, Centrale Marseille, I2M Marseille France |
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| Yi Liu | |
| Beijing International Center for
Mathematical Research Peking University Beijing China |
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| Hongbin Sun | |
| Department of Mathematics University of California Berkeley, CA United States |
Department of Mathematics Rutgers University Piscataway, NJ United States |
| Shicheng Wang | |
| School of Mathematical
Sciences Peking University Beijing China |
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