# Hopf invariants, topological complexity, and LS-category of the cofiber of the diagonal map for two-cell complexes

Jesús González, Mark Grant, Lucile Vandembroucq

Research output: Chapter in Book/Report/Conference proceedingPublished conference contribution

2 Citations (Scopus)

## Abstract

Let $X$ be a two-cell complex with attaching map $\alpha\colon S^q\to S^p$, and let $C_X$ be the cofiber of the diagonal inclusion $X\to X\times X$. It is shown that the topological complexity (${\rm TC}$) of $X$ agrees with the Lusternik-Schnirelmann category (${\rm cat}$) of $C_X$ in the (almost stable) range $q\leq2p-1$. In addition, the equality ${\rm TC}(X)={\rm cat}(C_X)$ is proved in the (strict) metastable range \$2p-1
Original language English Topological complexity and related topics Mark Grant, Gregory Lupton, Lucile Vandembroucq American Mathematical Society 133-150 18 702 9781470444051 9781470434366 https://doi.org/10.1090/conm/702/14109 Published - 2018

### Publication series

Name Contemporary Mathematics American Mathematical Society 1098-3627 0271-4132

## Keywords

• math.AT
• 55M30, 55Q25, 55S35, 55S36, 68T40, 70B15

## Fingerprint

Dive into the research topics of 'Hopf invariants, topological complexity, and LS-category of the cofiber of the diagonal map for two-cell complexes'. Together they form a unique fingerprint.