On Geometry and Topology of 4-Orbifolds

TL;DR

This paper investigates the geometric and topological properties of 4-dimensional orbifolds with positive curvature, establishing analogues of known results and exploring the implications of fundamental groups on Poincaré Duality.

Contribution

It extends classical results to 4-orbifolds, linking curvature, symmetry, and fundamental group properties to topological duality conditions.

Findings

Proves an analogue of Hsiang and Kleiner's result for 4-orbifolds with positive curvature.

Shows the orbifold fundamental group bounds the failure of integer-valued Poincaré Duality.

Establishes that simply connected orbifolds satisfy integer-valued Poincaré Duality.

Abstract

We prove an analogue of the result of Hsiang and Kleiner for 4-dimensional compact orbifolds with positive curvature and an isometric circle action. Additionally, we prove that when the underlying space is simply connected, then the orbifold fundamental group provides a bound on the failure of integer-valued Poincare Duality of the underlying space, and if the orbifold is simply connected, then ineteger-valued Poincre Duality holds for the underlying space.