Geodesic
Explicit rank bounds for cyclic covers
DeBlois, Jason1
1Department of Mathematics, University of Pittsburgh, 301 Thackeray Hall, Pittsburgh, PA 15260, United States
Algebraic and Geometric Topology, Tome 16 (2016) no. 3, pp. 1343-1371
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For a closed, orientable hyperbolic 3–manifold M and an onto homomorphism ϕ: π1(M) → ℤ that is not induced by a fibration M → S1, we bound the ranks of the subgroups ϕ−1(nℤ) for n ∈ ℕ, below, linearly in n. The key new ingredient is the following result: if M is a closed, orientable hyperbolic 3–manifold and S is a connected, two-sided incompressible surface of genus g that is not a fiber or semifiber, then a reduced homotopy in (M,S) has length at most 14g − 12.

DOI : 10.2140/agt.2016.16.1343
Classification : 20F05, 57M10, 20E06
Keywords: rank, rank gradient, JSJ decomposition

DeBlois, Jason  1

1 Department of Mathematics, University of Pittsburgh, 301 Thackeray Hall, Pittsburgh, PA 15260, United States 
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DeBlois, Jason. Explicit rank bounds for cyclic covers. Algebraic and Geometric Topology, Tome 16 (2016) no. 3, pp. 1343-1371. doi: 10.2140/agt.2016.16.1343

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