Jamie Scott - Applications of Surgery to a Generalized Rudyak Conjecture
Offered By: Applied Algebraic Topology Network via YouTube
Course Description
Overview
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.
Syllabus
Introduction
Sectional Categories
Motion Planning
Rudyak Conjecture
Embeddings of Spheres
Homotopic equivalence
Example A
Surge Restrictions
Simply Connected
Two Cases
Lemma
Web Product
Taught by
Applied Algebraic Topology Network
Related Courses
Autodiagnosis and the Dynamical Emergence Theory of Basic ConsciousnessSanta Fe Institute via YouTube Surfaces in 3-Manifolds and the Thurston Norm
Fields Institute via YouTube Enrique Torres-Giese - Sequential Motion Planning Assisted by Group Actions
Applied Algebraic Topology Network via YouTube Steve Scheirer - Relative Topological Complexity and Configuration Spaces
Applied Algebraic Topology Network via YouTube Effectual Topological Complexity
Applied Algebraic Topology Network via YouTube