3-manifold spine cyclic presentations with seldom seen Whitehead graphs

Abstract

We consider two families of cyclic presentations and show that, subject to certain conditions on the defining parameters, they are spines of closed 3-manifolds. For the first family, the Whitehead graphs have not previously been observed in this context, and the corresponding manifolds are lens spaces. The second family provides new examples where the reduced Whitehead graphs are those of the Fractional Fibonacci presentations; here the corresponding manifolds are often (but not always) hyperbolic.