Splice diagrams and splice-quotient surface singularities

2022/02/01 by Jonathan Wahl, Wahl, Jonathan
Mathematics · #14B05 #14J17 #32S25 #32S50 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2202.00587

openalex publication_date 2022/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The current work will appear in a Celebratio Mathematica volume in honor of Walter Neumann. We summarize results and methods from our long-time collaboration with Neumann, especially the motivation for the introduction of splice diagrams to define singularities of splice type and splice-quotient singularities. The Casson Invariant Conjecture and Milnor Fiber Conjectures are discussed, as well as some open questions about hypersurface and complete intersection singularities with integral homology sphere link.

Related

• On the Casson Invariant Conjecture of Neumann--Wahl
• On the topology of surface singularities zⁿ=f(x,y), for f irreducible
• Geometry of splice-quotient singularities
• The cohomology of line bundles of splice-quotient singularities
• The Milnor fiber conjecture of Neumann and Wahl, and an overview of its proof