Homology of dihedral quandles
Maciej Niebrzydowski, Jozef H. Przytycki
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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