Topological Complexity of wedges

TL;DR

This paper establishes a formula for the topological complexity of wedge spaces, relating it to the complexities of individual spaces and their product, advancing the understanding of motion planning in topological spaces.

Contribution

It provides a new explicit formula for the topological complexity of wedge sums, connecting it with the complexities of component spaces and their Cartesian product.

Findings

Topological complexity of wedge spaces is given by a maximum involving component complexities.

The formula links topological complexity with Lusternik–Schnirelmann category of the product.

This result simplifies calculations of topological complexity for wedge spaces.

Abstract

We prove the formula \begin{equation*} TC(X\vee Y)=\max\{TC(X),TC(Y),cat(X\times Y)\} \end{equation*} for the topological complexity of the wedge $X\vee Y$.