How highly connected can an orbifold be?

TL;DR

This paper constructs examples of highly connected bad orbifolds and proves that n-connected n-orbifolds are manifolds, improving previous bounds and providing sharp results up to dimension 5.

Contribution

It introduces the first examples of highly connected bad orbifolds and establishes new bounds showing n-connected n-orbifolds are manifolds, refining earlier results.

Findings

Constructed arbitrarily highly connected bad orbifolds.

Proved n-connected n-orbifolds are manifolds, improving previous bounds.

Achieved sharp bounds up to dimension 5.

Abstract

On the one hand, we provide the first examples of arbitrarily highly connected (compact) bad orbifolds. On the other hand, we show that n-connected n-orbifolds are manifolds. The latter improves the best previously known bound of Lytchak by roughly a factor of 2. For compact orbifolds and in most dimensions we prove slightly better bounds. We obtain sharp results up to dimension 5.