Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 16, Number 3 (2016), 1343-1371.
Explicit rank bounds for cyclic covers
For a closed, orientable hyperbolic –manifold and an onto homomorphism that is not induced by a fibration , we bound the ranks of the subgroups for , below, linearly in . The key new ingredient is the following result: if is a closed, orientable hyperbolic –manifold and is a connected, two-sided incompressible surface of genus that is not a fiber or semifiber, then a reduced homotopy in has length at most .
Algebr. Geom. Topol., Volume 16, Number 3 (2016), 1343-1371.
Received: 4 November 2013
Revised: 19 October 2015
Accepted: 4 November 2015
First available in Project Euclid: 28 November 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 20F05: Generators, relations, and presentations 57M10: Covering spaces
Secondary: 20E06: Free products, free products with amalgamation, Higman-Neumann- Neumann extensions, and generalizations
DeBlois, Jason. Explicit rank bounds for cyclic covers. Algebr. Geom. Topol. 16 (2016), no. 3, 1343--1371. doi:10.2140/agt.2016.16.1343. https://projecteuclid.org/euclid.agt/1511895848