Moving homology classes in finite covers of graphs


DOI: 10.1007/s11856-017-1528-5

Cite this article as:
Farb, B. & Hensel, S. Isr. J. Math. (2017). doi:10.1007/s11856-017-1528-5


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 \(\left\{ {{{\widetilde F}^d}\left( v \right):d \in \mathbb{Z}} \right\} \subseteq {H_1}\left( {Y;\mathbb{Q}} \right)\) 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.

Copyright information

© Hebrew University of Jerusalem 2017

Authors and Affiliations

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

Personalised recommendations