Knots, Links, and 4-Manifolds

1996/12/18 by Fintushel, Ronald, Stern, Ronald J. · 5 citations
#Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.dg-ga/9612014

Abstract

In this paper we investigate the relationship between isotopy classes of knots and links in S³ and the diffeomorphism types of homeomorphic smooth 4-manifolds. As a corollary of this initial investigation, we begin to uncover the surprisingly rich structure of diffeomorphism types of manifolds homeomorphic to the K3 surface.

Cited by

• Trisections and Lefschetz fibrations with (-n)-sections
• Extending Fibrations of the 3-Torus and Applications to Torus Surgery in 4-Manifolds
• The Boundary Dehn Twist on a Punctured Connected Sum of Two K3 Surfaces is Nontrivial in the Smooth Mapping Class Group
• Constraints on Lefschetz fibrations with four-dimensional fibers from Seiberg-Witten theory
• Irreducible 4-manifolds with order two fundamental group and even intersection form

Related

• Some 4-manifold geometry from hyperbolic knots in S³
• Theta-graph and diffeomorphisms of some 4-manifolds
• Exotic knottings and symmetries of surfaces in 4-manifolds
• The salient crossings of a crown diagram
• Invariants of surfaces in smooth 4-manifolds from link homology