Some open 3-manifolds and 3-orbifolds without locally finite canonical decompositions

TL;DR

This paper presents examples of open 3-manifolds and 3-orbifolds that demonstrate unusual splitting behavior along certain surfaces, challenging existing understandings of their canonical decompositions.

Contribution

It introduces specific examples of open 3-manifolds and 3-orbifolds with pathological splitting properties, highlighting limitations of current decomposition theories.

Findings

Examples of open 3-manifolds without locally finite canonical decompositions

Examples of 3-orbifolds with similar pathological behavior

Insights into the complexity of splitting along nonnegative Euler characteristic surfaces

Abstract

We give examples of open 3-manifolds and 3-orbifolds that exhibit pathological behavior with respect to splitting along surfaces (2-suborbifolds) with nonnegative Euler characteristic.