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In this paper we prove the Milnor Fiber Conjecture of Neumann and Wahl for a class of isolated complete intersection singularities obtained by taking iterated branched cyclic covers of the singularity link. We also show that if the Milnor Fiber Conjecture holds for a given splice diagram, then it holds for any equivalent diagram satisfying the semigroup condition. We illustrate the application of these theorems in an example and discuss the relationship of these singularities with Neumann and Wahl's Splice Type Conjecture. The local topology of a normal complex surface singularity is completely de- termined by a canonically associated 3-manifold called the link of the singularity. Michael Artin first asked the question: What analytic invariants of the singularity are determined by the topology and when? Since Artin's question, many conjec- tures have appeared suggesting a strong relationship between the analytic invariants of such a singularity and its topology under certain restricting assumptions on the topology of the link (e.g. (10, 11, 12, 13, 18, 19)). These conjectures overlap at vary- ing levels of generality and provide both motivation and support for one another. Several of the conjectures have been verified for large families of singularities. Re- cently however, counterexamples have been discovered to many of these conjectures by Luengo-Velasco, Melle-Hernandez and Nemethi (8).

The Milnor Fiber Conjecture and iterated branched cyclic covers