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The current work will appear in a Celebratio Mathematica volume in honor ofWalter Neumann. We summarize results and methods from our long-timecollaboration with Neumann, especially the motivation for the introduction ofsplice diagrams to define singularities of splice type and splice-quotientsingularities. The Casson Invariant Conjecture and Milnor Fiber Conjectures arediscussed, as well as some open questions about hypersurface and completeintersection singularities with integral homology sphere link.

Splice diagrams and splice-quotient surface singularities