IPDF Seminar
Tuesday, 18 April 2023, 2.30 pm
=========================
Venue: Ramanujan Hall
Host: Rekha Santhanam
Speaker: Navnath Daundkar
Affiliation: IIT Bombay
Title: Topological Complexity of fibre bundles, lower bounds on higher topological complexity and its Applications
Abstract: For a path-connected space, Farber introduced a numerical homotopy invariant called topological complexity. Farber gave an additive upper bound on the topological complexity of product spaces. In the first part of this talk, we show that fibre bundles have such an upper bound under certain conditions. As an application, we obtain a tight upper bound on the topological complexity of higher-dimensional Klein bottles. This is based on the joint work with Prof. Soumen Sarkar. In the next part of this talk, we study a higher analogue of topological complexity. Here we improve the usual cohomological lower bound by introducing the concept of higher TC-weights. Then we use this to show that nth topological complexity of Seifert fibre manifolds is either 3n or 3n+1. This is based on joint work with Prof. Rekha Santhanam and Soumyadip Thandar.