The fibrewise method in topological complexity and its variants

• Grant number: 19/20061-0
• Support Opportunities: Scholarships abroad - Research Internship - Master's degree
• Start date: February 01, 2020
• End date: May 24, 2020
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Denise de Mattos
• Grantee: Matias de Jong van Lier
• Supervisor: Norio Iwase
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Institution abroad: Kyushu University, Japan
• Associated to the scholarship: 18/23410-3 - Topological complexity and Lusternik-Schnirelmann category, BP.MS

Abstract

This research project's main goal is to study the fibrewise method for topological complexity,while tackling some interesting open problems such as: (1) the existence of a relation among fibrewise category, fibrewise pointed category and the various forms of topological complexity; (2) the question whether cat_B(X) = cat_B^B(X) for X a fibrewise well-pointed space; (3) the relation between TC(X) and TC^M(X) for X a finite Delta-complex, or a finite CW-complex. (AU)