Families of four dimensional manifolds that become mutually diffeomorphic after one stabilization
D. Auckly
Abstract
In this paper, we will introduce a cut and paste move, called a geometrically null log transform, and prove that any two manifolds related by a sequence of these moves become diffeomorphic afte r one stabilization. To motivate the cut and paste move, we will use the symplec tic fiber sum, and a construction of Fintushel and Stern to construct several large families of 4-manifolds. We will then proceed to prove that the members of any one of these families become diffeomorphic after one stabilization. Finally, we will compute the Seiberg-Witten invariants of each member of each of the families.
Create a lesson
Related papers
Using Transformers to Generate 3-Manifold Triangulations
Daniel Bruwel, Ashvni Narayanan, Jonathan Spreer
The residual map as a stratified fibration over the resonance arrangement
Dawei Chen, Scott Mullane, Nick Salter et al.
Chromatic Spherical and Renormalized Reshetikhin-Turaev Invariants for Drinfeld Centers
Nicolas Bridges, Shawn Cui, Nathan Geer
3-manifold decision problems and Riemann hypotheses
John A. Baldwin, Steven Sivek
On the (in)finiteness of fixed characters in genus 3
Yixuan Fu
Non-Pseudo-Arithmetic Hyperbolic 4-Manifolds
Alexander Kolpakov