Homology of dihedral quandles

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 pp odd prime [T. Ohtsuki, Problems on invariants of knots and 3-manifolds, Geom. Topol. Monogr. 4 (2002) 377-572, Conjecture 5.12]. We also show that HnR(Rp) contains ZpZp for n≥3n≥3. Furthermore, we show that the torsion of HnR(R3) is annihilated by 3. We also prove that the quandle homology H4Q(Rp) contains ZpZp for pp odd prime. We conjecture that for n>1n>1 quandle homology satisfies: HnQ(Rp)=Zpfn, where fnfn are “delayed” Fibonacci numbers, that is, fn=fn−1+fn−3fn=fn−1+fn−3 and f(1)=f(2)=0,f(3)=1f(1)=f(2)=0,f(3)=1. Our paper is the first step in approaching this conjecture.