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Based on Morse homology of Morse functions, we give a new proof of the Morse-Bott inequalities for functions with non-degenerate critical manifolds.^[1]
In mathematics, specifically in the field of differential topology, Morse homology is a homology theory defined for any smooth manifold.^[2]
Another approach to proving the invariance of Morse homology is to relate it directly to singular homology.^[2]
The associated Morse homology is an invariant for the manifold, and equals the singular homology, which yields the classical Morse relations.^[3]
Morse homology were developed during the rst half of the twentieth century.^[4]
The Morse Homology Theorem.- Morse Theory on Grassmann Manifolds.- An Overview of Floer Homology Theories.- Hints and References for Selected Problems.- Bibliography.- Symbol Index.- Index.^[5]
Hutchings’ approach to the Leray-Serre spectral sequence in Morse homology couples a fiberwise negative gradient flow with a lifted negative gradient flow on the base.^[6]
We study the Morse homology of a vector field that is not of gradient type.^[6]
This problems seems difficult, and the only reference I have found is Schwarz' Morse Homology.^[7]
This book offers a detailed presentation of results needed to prove the Morse Homology Theorem using classical techniques from algebraic topology and homotopy theory.^[8]
This book presents in great detail all the results one needs to prove the Morse Homology theorem … .^[9]