An upper bound for the Lusternik-Schnirelmann category of relative Sullivan algebras

TL;DR

This paper establishes an upper bound for the Lusternik-Schnirelmann category of relative Sullivan algebras, linking it to the finiteness of the invariants of base and fiber algebras, and also estimates the Toomer invariant.

Contribution

It provides a new upper bound for the LS-category of relative Sullivan algebras based on the invariants of base and fiber algebras, answering a question by Felix, Halperin, and Thomas.

Findings

LS-category is finite if base and fiber invariants are finite

Provides an estimation for the Toomer invariant

Answers an open question in the field

Abstract

This paper addresses a question posed by F\'elix, Halperin and Thomas. We prove that the Lusternik-Schnirelmann category of a relative Sullivan algebra is finite if such invariants of the base algebra and fiber algebra are both finite. Furthermore, we provide a similar estimation for the Toomer invariant.