Holed cone structures on 3-manifolds

TL;DR

This paper introduces holed cone structures on 3-manifolds, generalizing cone structures, and studies their deformation space related to holonomy representations, especially for positive cone angles.

Contribution

It defines holed cone structures, explores their properties, and analyzes the deformation space linked to irreducible holonomy representations.

Findings

Deformation space for positive cone angles forms a covering space.

Holed cone structures generalize traditional cone structures.

Holonomy representations are central to the structure's properties.

Abstract

We introduce holed cone structures on 3-manifolds to generalize cone structures. In the same way as a cone structure, a holed cone structure induces the holonomy representation. We consider the deformation space consisting of the holed cone structures on a 3-manifold whose holonomy representations are irreducible. This deformation space for positive cone angles is a covering space on a reasonable subspace of the character variety.