Maps on 3-manifolds given by surgery
Boldizsar Kalmar, Andras I. Stipsicz

TL;DR
This paper constructs stable maps from 3-manifolds obtained by surgery to the plane, providing bounds on singularities and fiber components based on the link properties.
Contribution
It introduces a method to produce stable maps for 3-manifolds from surgery diagrams and establishes bounds related to the link structure.
Findings
Upper bounds for crossings and singularities
Bounds on connected components of fibers
Construction of stable maps from surgery presentations
Abstract
Suppose that the 3-manifold M is given by integral surgery along a link L in S^3. In the following we construct a stable map from M to the plane, whose singular set is canonically oriented. We obtain upper bounds for the minimal numbers of crossings and non-simple singularities and of connected components of fibers of stable maps from M to the plane in terms of properties of L.
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Taxonomy
TopicsGeometric and Algebraic Topology · Mathematical Dynamics and Fractals · Geometric Analysis and Curvature Flows
