 

Benson Farb and Sebastian Hensel
Finite covers of graphs, their primitive homology, and representation theory view print


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


Abstract
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 H_{1}(Y;C) as a Grepresentation. A central object in this study is the primitive homology group H_{1}^{prim}(Y;C)⊆
H_{1}(Y;C), which is the span of homology classes represented by components of lifts of primitive elements of π_{1}(X). This circle of ideas relates combinatorial group theory, surface topology, and representation theory.


Acknowledgements
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
farb@math.uchicago.edu
Sebastian Hensel:
Mathematisches Institut, Rheinische FriedrichWilhelmsUniversität Bonn, Endenicher Allee 60, 53115 Bonn, Germany
hensel@math.unibonn.de

