A short proof for tc(K) = 4

TL;DR

This paper presents a novel fibrewise approach to determine the topological complexity of the Klein bottle, providing an alternative proof that tc(K) equals 4.

Contribution

It introduces a new fibrewise method to compute topological complexity, offering an alternative proof for the Klein bottle case.

Findings

Topological complexity of Klein bottle is 4

Fibrewise perspective offers new proof techniques

Method may extend to other non-orientable surfaces

Abstract

We show a method to determine topological complexity from the fibrewise view point, which provides an alternative proof for tc(K) = 4, where K denotes Klein bottle.