On the impossibility of four-dimensional complex-hyperbolic Einstein Dehn filling

TL;DR

This paper proves that it is impossible to perform complex-hyperbolic Einstein Dehn filling compactification in four-dimensional spaces, highlighting fundamental limitations in this geometric process.

Contribution

It establishes a fundamental impossibility result for four-dimensional complex-hyperbolic Einstein Dehn filling.

Findings

Dehn filling compactification cannot be performed in dimension four

The result constrains the scope of complex-hyperbolic Einstein geometry

Provides insights into geometric limitations in four dimensions

Abstract

We show that the complex-hyperbolic Einstein Dehn filling compactification cannot possibly be performed in dimension four.