Paper Moebius bands with T Patterns

TL;DR

This paper provides an alternative, more geometrically intuitive proof of a key lemma that resolves the optimal paper Moebius band conjecture, advancing understanding in geometric topology.

Contribution

It offers a longer, more intuitive proof of the key lemma in the conjecture, enhancing geometric understanding.

Findings

Proof of the key lemma confirming the conjecture

Enhanced geometric intuition for Moebius band properties

Validation of the optimality conditions for paper Moebius bands

Abstract

This paper gives another proof of the key lemma in my recent paper which solves the optimal paper Moebius band conjecture of Halpern and Weaver, namely Lemma T. The proof here is longer but it offers more geometric intuition about what is going on.