Pinwheels and nullhomologous surgery on 4-manifolds with b^+ = 1

TL;DR

This paper introduces a method to alter the smooth structure of 4-manifolds with b^+ = 1 by performing surgery on embedded nullhomologous tori, leading to new infinite families of such manifolds.

Contribution

It provides a novel technique for finding nullhomologous tori in standard 4-manifolds and applying surgery to generate diverse smooth structures.

Findings

Constructed infinite families of simply connected 4-manifolds with specified Betti numbers.

Demonstrated the existence of embedded nullhomologous tori in standard 4-manifolds.

Showed how surgery on these tori changes the smooth structure.

Abstract

We present a method for finding embedded nullhomologous tori in standard 4-manifolds which can be utilized to change their smooth structure. As an application, we show how to obtain infinite families of simply connected smooth 4-manifolds with b^+ = 1 and b^- = 2,...,7, via surgery on nullhomologous tori embedded in the standard manifolds CP^2 # k (-CP^2), k=2,...,7.