Riemannian foliation with exotic tori as leaves

TL;DR

This paper constructs examples of Riemannian foliations on closed manifolds with exotic tori as leaves, demonstrating new geometric structures with finite abelian fundamental groups.

Contribution

It introduces smooth fiber bundles with exotic tori as fibers and finite abelian fundamental groups, providing novel examples of Riemannian foliations.

Findings

Existence of smooth fiber bundles with exotic tori as fibers.

Construction of Riemannian foliations with exotic leaves.

Total space has finite abelian fundamental group.

Abstract

We construct smooth fiber bundles such that the fibers are exotic tori and the total space has finite abelian fundamental group. This gives examples of a Riemannian foliation on a closed manifold whose leaves are exotic tori and whose total space has finite abelian fundamental group.