NCN PRELUDIUM 21

During my PhD studies in Adam Mickiewicz University I was principal investigator of the Polish National Center of Science grant 2022/45/N/ST1/02814 PRELUDIUM.

Title of the project

Topological robotics: topological complexity of K(G,1) spaces and effective topological complexity

Duration

24 months

Hosting Institution

Adam Mickiewicz University

Short description

In this project I studied different aspects of the relationship between groups and topological complexity (TC) and related category-like invariants. The approach was on two different fronts:

• The study of (sequential) topological complexity of spaces of type K(G,1) for G a torsion-free discreet group, and of sectional category of fibrations between K(G,1) spaces that are induced by subgroup inclusions.
• The study of how symmetries (mathematically encoded as group actions) can help in reducing the complexity of the motion planning by investigating the properties of an equivariant version of the classic TC, called effective topological complexity.
• Description for the general public

Results of the project

(You can see more details on the following papers in the section Research )

• Sequential topological complexity of aspherical spaces and sectional categories of subgroup inclusions. with M. Farber, S. Mescher and J. Oprea.
• On properties of effective topological complexity and effective Lusternik-Schnirelmann category. with Z. Błaszczyk and A. Viruel.
• Sectional category of subgroup inclusions and sequential topological complexities of aspherical spaces as A-genus.

You can access the official entry of this grant in the NCN database following the next LINK .