Families of four dimensional manifolds that become mutually diffeomorphic after one stabilization

2000/09/29 by D. Auckly, Auckly, D.
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #math.GT

paper · pdf · doi:10.48550/arxiv.math/0009248

23 pages, 30 figures

arxiv created 2000/09/29 · arxiv updated 2009/11/30

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.

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