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

References in corpus (1)

• Topological Index Theory for Surfaces in 3-Manifolds

Cited by in corpus (5)

• Topological Index Theory for Surfaces in 3-Manifolds
• Heegaard splittings of sufficiently complicated 3-manifolds I: Stabilization
• Heegaard splittings of sufficiently complicated 3-manifolds II: Amalgamation
• A note on the nearly additivity of knot width
• Stabilization, amalgamation, and curves of intersection of Heegaard splittings