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Results tagged with smooth-manifolds
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user 124549
Smooth manifolds and smooth functions between them. For manifolds with additional structure, see more specific tags, such as [riemannian-geometry]. For more topological aspects, see [differential-topology].
20
votes
1
answer
591
views
Manifolds as Cauchy completed objects
The category of smooth manifolds (SmoothMfld) can be thought of the Cauchy completion of the category $U$ of open subsets of Euclidean spaces (with smooth maps) [1]. This fact is shocking to me as it …
- 5,230
4
votes
0
answers
382
views
Obstruction of smooth structure
The first 24 lectures of Jacob Lurie on Geometric Topology [1]
gave a concise introduction to the comparison of smooth manifolds
and piecewise-linear manifold. In the first five lectures, it is
shown …
- 5,230
4
votes
0
answers
360
views
Kirby's theorem for 4-manifolds
In dimension 3, we have the celebrated Kirby theorem: Let $L_1, L_2$ be two links in the 3-sphere $S^3$; then they surgeries along them produce homeomorphic 3-manifolds if and only if they are related …
- 5,230
9
votes
0
answers
202
views
Donaldson invariants for piecewise-linear $4$-manifolds
It is well known that in dimension $4$, the notion of piecewise linear manifolds and the notion of smooth manifolds are the same [1][2]. On the other hand, the computations of Donaldson invariants inv …
- 5,230
8
votes
2
answers
590
views
Presentations of exotic 4-manifolds
TLDR I want to see more examples of exotic $4$-manifold (hopefully connected, simply connected, oriented, and closed).
Are there known presentations of $4$-manifolds $M$ with exotic structures, whethe …
- 5,230