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Benson Farb and Sebastian Hensel
Finite covers of graphs, their primitive homology, and representation theory view print
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| Published: |
November 15, 2016 |
| Keywords: |
Homology of finite covers, Chevalley-Weil Theorem, primitive homology |
| Subject: |
20F34, 57M07, 57M10 |
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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 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.
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| Acknowledgements
The first author gratefully acknowledges support from the National Science Foundation.
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| 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 Friedrich-Wilhelms-Universität Bonn, Endenicher Allee 60, 53115 Bonn, Germany
hensel@math.uni-bonn.de
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