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Results tagged with morse-theory
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user 8032
In differential topology, Morse theory enables one to analyze the topology of a manifold by studying differentiable functions on that manifold.
1
vote
What does it mean that homotopy is generic?
"Generic" usually refers to open and dense.
Assume $M$ is a closed smooth manifold. Let $$C^\infty(M)$$ be the space of all smooth real valued functions. Topologize this with respect to the Whitney …
- 18.5k
11
votes
Accepted
How does the Framed Function Theorem simplify Cerf Theory?
The framed function theorem tells you that up to "contractible choice" a compact manifold admits a framed function: i.e., a function as you prescribe. Furthermore, a framed function is supposed to giv …
- 18.5k
6
votes
Accepted
Constructing ($\infty, 1)$-category from Morse theory on a manifold
This problem has a long history going back at least to the paper of Cohen, Jones and Segal (available here: http://www.kurims.kyoto-u.ac.jp/~kyodo/kokyuroku/contents/pdf/0883-04.pdf).
In terms of your …
- 18.5k
6
votes
Searching for an unabridged proof of "The Basic Theorem of Morse Theory"
My recollection is that Milnor's proof gives exactly what you are asking. In fact, see the remark on the bottom of page 17 of his book.
- 18.5k
6
votes
Stratification of smooth maps from R^n to R?
It looks to me that what you are really interested in is the Thom-Boardman stratification of the function space. For that I would recommend the well-written, Stable Mappings and Their
Singularities b …
- 18.5k
14
votes
Unstable manifolds of a Morse function give a CW complex
(1). Some experts tell me that Laudenbach's paper is incomplete and contains gaps.
I will retract this for now. I do recall being told this, but I am not
aware at this point in time where the gaps …
- 18.5k