Israel Journal of Mathematics

, Volume 220, Issue 2, pp 605–615

Moving homology classes in finite covers of graphs



Let YX be a finite normal cover of a wedge of n ≥ 3 circles. We prove that for any nonzero vH1(Y; Q) there exists a lift \(\widetilde F\) to Y of a basepoint-preserving homotopy equivalence F: XX such that the set of iterates \(\left\{ {{{\widetilde F}^d}\left( v \right)} \right\}:d \in \mathbb{Z} \subseteq {H_1}\left( {Y,\mathbb{Q}} \right)\) 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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© Hebrew University of Jerusalem 2017

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of ChicagoChicagoUSA
  2. 2.Mathematisches InstitutRheinische Friedrich-Wilhelms-Universität BonnBonnGermany

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