Gravitational sources induced by exotic smoothness

TL;DR

This paper constructs a coordinate atlas for an exotic  using handlebody decomposition, revealing that exotic smoothness in  naturally induces a spinor field, linking topology to physical fields.

Contribution

It demonstrates that exotic smooth structures on  inherently generate spinor fields through handlebody and immersion constructions.

Findings

Exotic  admits a coordinate atlas via handlebody decomposition.

Immersion of the exotic  into  induces a natural spinor field.

Exotic smoothness in  can produce physical fields from topology.

Abstract

In this paper we construct a coordinate atlas in an exotic $\mathbb{R}^{4}$ using Bizaca's construction. The main source for such an atlas is the handle body decomposition of a Casson handle, which of course is an infinite, but periodic, process. The immersion of the end-periodic manifold into $\mathbb{R}^{4}$ is directly related to the exoticness of the $\mathbb{R}^{4}$ and also gives rise naturally to a spinor field. Thus we obtain the interesting result that the simplest exotic $\mathbb{R}^{4}$ generates an extra spinor field by exoticness.