Mathematical Sciences

Title :

Lusternik-Schnirelmann Category and several Topological Complexities, and their applications in robotics

Area of research :

Mathematical Sciences

Focus area :


Principal Investigator :

Dr. Soumen Sarkar, Associate Professor, Indian Institute of Technology (IIT), Madras

Timeline Start Year :


Contact info :


Executive Summary :

The LS-category, introduced in 1934, has been extensively studied in various fields, including variational calculus, manifolds, and CW-complexes. Topological complexity, a homotopy invariant, has been introduced in robotics, with higher, symmetric, D-topological, relative, and parametrized topological complexity being the most recent. The project aims to explore new theories in robot motion planning, investigate their practical applications, and compute topological complexities of these spaces.

Total Budget (INR):


Organizations involved