LS-Category and Topological Complexity of Real Torus Manifolds and Dold Manifolds

Explore advanced concepts in algebraic topology through this 42-minute conference talk that examines the LS-category and topological complexity of real torus manifolds and Dold manifolds of real torus type. Learn about real torus manifolds as generalizations of small covers, which serve as topological generalizations of smooth projective real toric varieties, and discover how Dold manifolds of real torus type function as non-trivial fibre bundles over projective product spaces with real torus manifolds as fibres. Follow the computation of exact LS-category values for both types of manifolds and examine the derivation of sharp bounds on their topological complexities. Understand how topological complexities of real torus manifolds of dimension n are either 2n or 2n+1 under certain hypotheses, and investigate bounds for the topological complexity of generalized real Bott manifolds where the difference between upper and lower bounds is often less than 5. Gain insights from joint research work with Navnath and Koushik presented by Soumen Sarkar as part of the Applied Algebraic Topology Network series.