Almost normal surfaces with boundary

TL;DR

This paper demonstrates that certain complex surfaces in triangulated 3-manifolds can be isotoped to an almost normal form, aiding in the understanding and classification of 3-manifold topology.

Contribution

It establishes that strongly irreducible and boundary-strongly irreducible surfaces can be isotoped to almost normal surfaces, extending normal surface theory.

Findings

Surfaces can be isotoped to almost normal form in specific conditions.

Provides a method to simplify the study of 3-manifold surfaces.

Enhances the toolkit for 3-manifold topologists.

Abstract

We show that a strongly irreducible and boundary-strongly irreducible surface can be isotoped to be almost normal in a triangulated 3-manifold.