Zeta functions of finite Schreier graphs and their zig zag products

2015/08/03 by Shaikh, Asif, Bhate, Hemant
#05C31 #05C50 #05C76 #20E08 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1508.00371

Abstract

We investigate the Ihara zeta functions of finite Schreier graphs Γ_n of the Basilica group. We show that Γ_1+n is 2 sheeted unramified normal covering of Γ_n, ~∀~ n ≥ 1 with Galois group (ℤ)/(2ℤ). In fact, for any n > 1, r ≥ 1 the graph Γ_n+r is 2ⁿ sheeted unramified, non normal covering of Γ_r. In order to do this we give the definition of the generalized replacement product of Schreier graphs. We also show the corresponding results in zig zag product of Schreier graphs Γ_n with a 4 cycle.

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