On the number of type change loci of a generalized complex structure

TL;DR

This paper presents a method to construct generalized complex structures with any desired number of type change loci on certain 4-manifolds, expanding the understanding of their geometric complexity.

Contribution

It introduces a procedure to generate generalized complex structures with arbitrarily many non-isotopic type change loci on specific 4-manifolds.

Findings

Constructed structures with multiple type change loci

Loci can be non-isotopic

Method applicable to products of circle and connected sums of 3-manifolds

Abstract

In this note, we describe a procedure to construct generalized complex structures with an arbitrarily large number of type change loci on products of the circle with a connected sum of closed 3-manifolds. The loci need not be isotopic.