Finite covers of graphs, their primitive homology, and representation theory
نویسندگان
چکیده
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 H 1 (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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تاریخ انتشار 2016