Cliff-wall surgery and vanishing of basic phase function for contractible topological Hamiltonian loop

TL;DR

This paper aimed to address a gap in a previous proof related to topological Hamiltonian loops but was withdrawn due to unresolved issues in the proof of a key lemma.

Contribution

It attempted to complete a proof regarding the behavior of the basic phase function for contractible topological Hamiltonian loops.

Findings

The paper was withdrawn due to a critical gap in the proof of Lemma 4.3.

No new results were established or published.

The work was an attempt to advance understanding of topological Hamiltonian loops.

Abstract

This note was an attempt to complete a gap in the proof of Theorem 11.1 of the paper arXiv:1111.5992. Due to a critical gap in the proof of Lemma 4.3, this paper is withdrawn.