Finiteness of purely cosmetic fillings

Key Points

• The study finds that there are only finitely many pairs of purely cosmetic fillings in certain 3-manifolds.
• Pairs of Dehn fillings maintain orientation-preserving homeomorphism in these cases, indicating specific topological properties.
• It focuses on unique characteristics of 3-manifolds, particularly concerning torus boundaries and incompressibility.
• This analysis enhances understanding around the behaviors of manifold fillings, highlighting constraints in manifold topology.

Abstract