Moving homology classes in finite covers of graphs

2015/09/30 by Benson Farb, Sebastian Hensel, Farb, Benson +1
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #math.GR #math.GT

paper · pdf · doi:10.48550/arxiv.1509.09253

8 pages; 1 figure

arxiv created 2015/09/30 · arxiv updated 2015/10/01

Abstract

Let Y→ X be a finite normal cover of a wedge of n≥ 3 circles. We prove that for any v≠ 0∈ H₁(Y;ℚ) there exists a lift \widetildeF to Y of a homotopy equivalence F:X→ X so that the set of iterates \\widetildeF^d(v): d∈ ℤ\⊆ H₁(Y;ℚ) is infinite. The main achievement of this paper is the use of representation theory to prove the existence of a purely topological object that seems to be inaccessible via topology.

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