Morse–Bott Theory and Diameters of Immersed Submanifolds of Euclidean Space
Open Access
Author:
Ginsburg, Victor
Area of Honors:
Mathematics
Degree:
Bachelor of Science
Document Type:
Thesis
Thesis Supervisors:
Sergei Tabachnikov, Thesis Supervisor Nathanial Patrick Brown, Thesis Honors Advisor
Keywords:
Morse theory Morse–Bott theory diameters double normals
Abstract:
We lay the groundwork for Morse–Bott theory, which we then apply to obtain two lower bounds
for the number of diameters of an immersed submanifold of Euclidean space. The sharper of the
two estimates is due to Pushkar’, and essentially marks the conclusion to this classical
problem.
