Flat fully augmented links are determined by their complements

2023/02/03 by Millichap, Christian, Trapp, Rolland · 1 citation
#57K10 #57K32 #57M50 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2302.02002

Abstract

In this paper, we show that two flat fully augmented links with homeomorphic complements must be equivalent as links in \mathbbS³. This requires a careful analysis of how totally geodesic surfaces and cusps intersect in these link complements and behave under homeomorphism. One consequence of this analysis is a complete classification of flat fully augmented link complements that admit multiple reflection surfaces. In addition, our work classifies those symmetries of flat fully augmented link complements which are not induced by symmetries of the corresponding link.

Cited by

• Symmetry groups of flat fully augmented links and their complements

Related

• Intercusp Geodesics and Cusp Shapes of Fully Augmented Links
• Geometry of fully augmented links in doubled 3-manifolds
• Symmetry groups of flat fully augmented links and their complements
• Standard position for surfaces in link complements in arbitrary 3-manifolds
• When do links admit homeomorphic C-complexes?