Barriers to Topologically Minimal Surfaces

Abstract

In earlier work we introduced topologically minimal surfaces as the analogue of geometrically minimal surfaces. Here we strengthen the analogy by showing that complicated amalgamations act as barriers to low genus, topologically minimal surfaces.

13 pages, 1 figure

Cited by in corpus (2)

• Heegaard splittings of sufficiently complicated 3-manifolds I: Stabilization
• Heegaard splittings of sufficiently complicated 3-manifolds II: Amalgamation