General Information
Seminar Class Name: Morse Theory & Topology
Aims: To introduce the basic Morse theory and its applications to topology, including the Morse functions, Morse lemma, cellular decomposition, Morse homolgy and their applications, this is a precourse to the Floer homology.
Main References: Michele Audin, Morse Theory and Floer Homology, Springer-Verlag
Time & Place: 2:00pm-4:00pm every Wednesday, Autumn Semester 2021 (Sep.5th-Christmas), Room 510, Department of Mathematics, Capital Normal University.
Titles and Speakers
Introduction: Symmetry in Symplectic Geometry
Speaker: Prof.Shanzhong Sun Date: 1st week
Beamer: T.B.A
Morse Functions and Their Existence
Speaker: Jinghong Deng Date: 2nd week
Morse Lemma and The Index of a Critical Points
Speaker: Zhengtong Xie Date: 3rd week
The Pseudo Gradients
Speaker: Hongjie Chow Date: 4th week
The Cellular Decomposition via the Critical Points
Speaker: Zhiyuan Liu Date: 4th week
The Smale Conditions with Examples
Speaker: Wen Shen Date: 6th week
The Existence of Smale Conditions
Speaker: Jia Fei Date: 7th week
An Introduction to Morse Homology
Speaker: Sanghao Xing Date: 8th week
The Indepence of the Choice of Morse Functions and the Pseudo Gradients
Speaker: Zhengtong Xie & Jinghong Deng Date: 9-10th week
Kunneth Formula, Poincare’s Duality, Euler Characteristic & Poincare’s Polynomail
Speaker: Zhiyuan Liu Date: 11th week
Morse Homology and the Connectedness
Speaker: Wen Shen Date: 13th week
Functoriality of Morse Homology
Speaker: Sanghao Xing Date: 14th week
The Long Exact Sequence
Speaker: Jia Fei Date: 15th week
An introduction to Arnold Conjecture
Speaker: T.B.A Date: 16th week
My Tiny Math Home 