New York Journal of Mathematics
Volume 22 (2016) 1365-1391


Benson Farb and Sebastian Hensel

Finite covers of graphs, their primitive homology, and representation theory

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Published: November 15, 2016
Keywords: Homology of finite covers, Chevalley-Weil Theorem, primitive homology
Subject: 20F34, 57M07, 57M10

Consider a finite, regular cover Y→ X of finite graphs, with associated deck group G. We relate the topology of the cover to the structure of H1(Y;C) as a G-representation. A central object in this study is the primitive homology group H1prim(Y;C)⊆ H1(Y;C), which is the span of homology classes represented by components of lifts of primitive elements of π1(X). This circle of ideas relates combinatorial group theory, surface topology, and representation theory.


The first author gratefully acknowledges support from the National Science Foundation.

Author information

Benson Farb:
Department of Mathematics, University of Chicago, 5734 University Ave., Chicago, IL 60637

Sebastian Hensel:
Mathematisches Institut, Rheinische Friedrich-Wilhelms-Universität Bonn, Endenicher Allee 60, 53115 Bonn, Germany