Geometry & Topology
- Geom. Topol.
- Volume 21, Number 5 (2017), 3159-3190.
Positive simplicial volume implies virtually positive Seifert volume for $3$–manifolds
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.
Geom. Topol., Volume 21, Number 5 (2017), 3159-3190.
Received: 6 July 2016
Accepted: 23 December 2016
First available in Project Euclid: 16 November 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 57M50: Geometric structures on low-dimensional manifolds
Secondary: 51H20: Topological geometries on manifolds [See also 57-XX]
Derbez, Pierre; Liu, Yi; Sun, Hongbin; Wang, Shicheng. Positive simplicial volume implies virtually positive Seifert volume for $3$–manifolds. Geom. Topol. 21 (2017), no. 5, 3159--3190. doi:10.2140/gt.2017.21.3159. https://projecteuclid.org/euclid.gt/1510859285