Inductive LS cocategory and localisation

TL;DR

This paper establishes bounds on the inductive LS cocategory of nilpotent CW-complexes using their p-localizations, improves previous results, and shows its generic nature for certain H_0-spaces.

Contribution

It introduces bounds on inductive LS cocategory via p-localizations and demonstrates its generic property for 1-connected H_0-spaces.

Findings

Inductive LS cocategory is bounded by p-localizations.

Dualisation improves previous LS category results.

Inductive cocategory is generic for certain H_0-spaces.

Abstract

In this paper we prove that the inductive cocategory of a nilpotent $CW$-complex of finite type $X$, $\indcocat X$, is bounded above by an expression involving the inductive cocategory of the $p$-localisations of $X$. Our arguments can be dualised to LS category improving previous results by Cornea and Stanley. Finally, we show that the inductive cocategory is generic for 1-connected $H_0$-spaces of finite type.