An Almost Flat Spin$^c$ Manifold Bounds

TL;DR

This paper proves that all almost flat spin^c$ manifolds can be realized as boundaries of compact orientable manifolds, resolving a longstanding conjecture in differential geometry.

Contribution

It establishes that every almost flat spin^c$ manifold bounds a compact orientable manifold, confirming a conjecture by Farrell--Zdravkovska and S. T. Yau.

Findings

All almost flat spin^c$ manifolds bound a compact orientable manifold.

The result confirms a long-standing conjecture in the field.

Advances understanding of the topology of spin^c$ manifolds.

Abstract

We prove that every almost flat spin^$c$ manifold bounds a compact orientable manifold, thereby settling, in the spin^$c$ case, a long-standing conjecture of Farrell--Zdravkovska and S. T. Yau.