A new construction of 6-manifolds

TL;DR

This paper introduces a topological construction method for all simply-connected, spin, smooth 6-manifolds with torsion-free homology, utilizing 4-manifolds as building blocks and explicitly determining their invariants.

Contribution

It provides a novel topological framework to construct and classify 6-manifolds from 4-manifold building blocks, explicitly determining their invariants.

Findings

Constructs all such 6-manifolds using 4-manifolds

Determines invariants from intersection forms and homology classes

Provides explicit classification criteria

Abstract

This paper provides a topological method to construct all simply-connected, spin, smooth $6$-manifolds with torsion-free homology using simply-connected, smooth $4$-manifolds as building blocks. We explicitly determine the invariants that classify these $6$-manifolds from the intersection form and specific homology classes of the $4$-manifold building blocks.