Generalized topological complexity and its monoidal version

TL;DR

This paper surveys the extension of Lusternik-Schnirelmann category results to topological complexity and its monoidal version, highlighting key implications for understanding space invariants beyond open subsets.

Contribution

It extends Srinivasan's result from LS-category to topological complexity and monoidal topological complexity, broadening the scope of space invariants.

Findings

Extension of Srinivasan's result to topological complexity

Implications for space invariants beyond open subsets

Enhanced understanding of topological invariants

Abstract

In the context of the Lusternik-Schnirelmann category, researcher T. Srinivasan demonstrated that when the space under consideration is an absolute neighborhood retract, its category can be realized through arbitrary subsets, not necessarily open ones. The primary aim of this survey is to illustrate how this result has been extended to the case of topological complexity and its monoidal version, along with some of its most significant implications.