Bounds on Morse-Novikov Numbers of 3-Manifolds
Offered By: IMSA via YouTube
Course Description
Overview
Explore a lecture on bounding Morse-Novikov numbers of 3-manifolds, delivered by Ken Baker from the University of Miami. Delve into the minimum number of critical points among circle valued Morse functions in a homotopy class, prompted by Pajitnov's work. Examine hands-on bounds and discover a curious function on cohomology, illustrated through a toy model involving links in the thickened torus. Learn about height functions, mud areas, knot types, circular bridges, orientation, embedding, and critical points. Investigate compression bodies, incompressible structures, and current work in this field. This joint work with Fabiola Manjarrez-Gutierrez covers topics from introduction and outline to ad hoc methods, providing a comprehensive overview of this mathematical concept.
Syllabus
Introduction
Outline
Height Function
Mud Areas
Knot Types
Circular Bridges
Orientation
Embedding
Nonsymmetrical
Boundary
Critical Points
Cyclists
Compression Bodies
Incompressible Structures
Extra Balance
Current Work
Ad hoc Methods
Taught by
IMSA
Related Courses
From Turaev to Rokhlin via VOA Characters and Curve CountingIMSA via YouTube From Turaev to Rokhlin via VOA Characters and Curve Counting
IMSA via YouTube From Knots to Number Theory II
ICTP Mathematics via YouTube Slope Detection in 3-Manifolds
ICTP Mathematics via YouTube Jacob Rasmussen - Floer Homology of 3-Manifolds with Torus Boundary
International Mathematical Union via YouTube