On Poincare Duality for Orbifolds

TL;DR

This paper establishes Poincaré Duality for 4- and 5-dimensional orbifolds under the condition that their orbifold fundamental group matches that of the underlying space, linking algebraic and topological properties.

Contribution

It proves Poincaré Duality for certain orbifolds assuming the orbifold fundamental group equals the space's fundamental group, a novel connection in orbifold topology.

Findings

Poincaré Duality holds for 4- and 5-dimensional orbifolds under specific conditions.

The orbifold fundamental group condition is crucial for duality results.

The work bridges algebraic and topological aspects of orbifolds.

Abstract

In this paper we address the relation between the orbifold fundamental group and the topology of the underlying space. In particular, under the assumption that the orbifold fundamental group is equal to the fundamental group of the underlying space, we prove Poincar\'e Duality for orbifolds of dimension 4 and 5.