Abstract
We have seen in Sect. 2.2 how to use a Morse function on a compact manifold M to reconstruct the manifold, up to a diffeomorphism via a sequence of elementary operations, namely, handle attachments.
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Notes
- 1.
Typically, these submanifolds are not properly embedded. For example, the unit circle in plane with a point removed is a submanifold of the plane.
- 2.
The submanifold X need not be closed in M.
- 3.
The matrix − A describes the Hessian of the function f.
- 4.
Algebraic geometers would call this a birational map.
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© 2012 Springer Science+Business Media, LLC
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Nicolaescu, L. (2012). Morse-Smale Flows and Whitney Stratifications. In: An Invitation to Morse Theory. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-1105-5_4
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DOI: https://doi.org/10.1007/978-1-4614-1105-5_4
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