Jamie Scott - Applications of Surgery to a Generalized Rudyak Conjecture

Explore the applications of surgery theory to a generalized Rudyak Conjecture in this 50-minute lecture from the Applied Algebraic Topology Network. Delve into the recent paper "Surgery Approach to Rudyak's Conjecture" and examine the proven theorem relating to degree one maps between closed manifolds. Investigate the techniques used, including surgery theory, and their potential generalizations to higher topological complexity. Focus on the case of simply connected codomains, where surgery obstructions are more easily calculated. Learn about the proven version of the theorem for higher topological complexity when the dimension of N is not congruent to 0 modulo 4, and explore a weaker theorem for regular topological complexity when the dimension of N equals 4n. Cover topics such as sectional categories, motion planning, embeddings of spheres, homotopic equivalence, surge restrictions, and web products.