Boundaries of locally conformally flat manifolds in dimensions $4k$

TL;DR

This paper establishes global restrictions on the boundaries of certain high-dimensional manifolds, using eta invariants to determine which boundaries are possible for compact, locally conformally flat manifolds in dimensions divisible by four.

Contribution

It introduces new global restrictions on boundaries of locally conformally flat manifolds in dimensions 4k, based on eta invariants, extending understanding of their geometric and topological properties.

Findings

Boundaries must satisfy integrality conditions of eta invariants.

Restrictions are specific to dimensions divisible by four.

Provides criteria for possible boundary manifolds in high dimensions.

Abstract

We give global restrictions on the possible boundaries of compact, orientable, locally conformally flat manifolds of dimension $4k$ in terms of integrality of eta invariants.