2012/11/21 by Haydée Aguilar-Cabrera, Aguilar-Cabrera, Haydée
Mathematics · #Algebraic Geometry and Number Theory #Bar (unit) #Combinatorics #Fibration #Geometric and Algebraic Topology #Gravitational singularity #Holomorphic function #Homotopy #Homotopy and Cohomology in Algebraic Topology #Mathematical analysis #Mathematics #Monodromy #Physics #Pure mathematics #Singularity #Suspension (topology) #Topology (electrical circuits) #Type (biology) #math.AG #math.GT #msc:32S25 #msc:32S50 #msc:32S55 #msc:57M27
paper · pdf · doi:10.48550/arxiv.1211.5103
arxiv created 2012/11/21 · openalex publication_date 2012/11/21 · arxiv updated 2012/11/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article we study the topology of a family of real analytic germs F \colon (ℂ3,0) → (ℂ,0) with isolated critical point at 0, given by F(x,y,z)=f(x,y)g(x,y)+zr, where f and g are holomorphic, r ∈ ℤ+ and r ≥ 2. We describe the link LF as a graph manifold using its natural open book decomposition, related to the Milnor fibration of the map-germ f g and the description of its monodromy as a quasi-periodic diffeomorphism through its Nielsen invariants. Furthermore, such a germ F gives rise to a Milnor fibration (F)/(|F|) \colon \mathbbS5 ∖ LF → \mathbbS1. We present a join theorem, which allows us to describe the homotopy type of the Milnor fibre of F and we show some cases where the open book decomposition of \mathbbS5 given by the Milnor fibration of F cannot come from the Milnor fibration of a complex singularity in ℂ3.