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In mathematics, specifically in the field of differential topology, Morse homology is a homology theory defined for any smooth manifold. It is constructed using the smooth structure and an auxiliary metric on the manifold, but turns out to be topologically invariant, and is in fact isomorphic to singular homology.
A rapid course in Morse homology. Let X be a smooth compact manifold of dimension d, and let f : X → R be a smooth function. Question: What can f tell us about ...
INTRODUCTION: OVERVIEW OF MORSE HOMOLOGY. What are nice functions? We will consider the following setup: M = closed1 (smooth) m-dimensional ...
by Y Chen - Cited by 6 - Related articles
A Brief History of Morse Homology. Yanfeng Chen. Abstract. Morse theory was originally due to Marston Morse [5]. It gives us a method to study the topology of aLecture notes on Morse homology (with an eye towards Floer theory and pseudoholomorphic curves). Michael Hutchings. December 15, 2002. Abstract.
by M Landry - 2014 - Related articles
Morse homology. Michael Landry. April 2014. This is a supplementary note for a (1.4 Stable and unstable manifolds. 5. 1.5 Basic differential topology. 6. 1.6 Morse-Smale functions. 7. 1.7 The Morse Homology Theorem. 9. 1.8 Morse theory on ...
by S Mescher - 2018
Apr 26, 2018 - Except for notational conventions, a reader familiar with Morse homology might skip this chapter without disadvantages. There are several ...MORSE HOMOLOGY. GEORGE TORRES. Math 213a. Fall 2016. 1. Introduction. Morse theory studies smooth manifolds by looking at particular differentiable ...
Morse Functions and Morse Homology. Abhineet Agarwal/Sabrina Victor. April 2019. 1 Morse Functions. Let X be a finite dimensional compact smooth manifold, ...