Homology of dihedral quandles
Abstract
We solve the conjecture by R. Fenn, C. Rourke and B. Sanderson that the rack homology of dihedral quandles satisfies H3R(Rp) = Z Zp for p odd prime. We also show that HnR(Rp) contains Zp for n>2. Furthermore, we show that the torsion of HnR(R3) is annihilated by 3. We also prove that the quandle homology H4Q(Rp) contains Zp for p odd prime. We conjecture that for n>1 quandle homology satisfies: HnQ(Rp) = Zpfn, where fn are "delayed" Fibonacci numbers, that is, fn = fn-1 + fn-3 and f(1)=f(2)=0, f(3)=1. Our paper is the first step in approaching this conjecture.
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