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Results tagged with gt.geometric-topology
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user 167587
Topology of cell complexes and manifolds, classification of manifolds (e.g. smoothing, surgery), low dimensional topology (e.g. knot theory, invariants of 4-manifolds), embedding theory, combinatorial and PL topology, geometric group theory, infinite dimensional topology (e.g. Hilbert cube manifolds, theory of retracts).
17
votes
0
answers
585
views
Must the number of smooth structures be countable or continuum?
Let $M$ be a manifold. Must the number of non-diffeomorphic smooth structures on $M$ be either countable or continuum? Could it be something in between when the continuum hypothesis fails?
Edit:
By m …
- 623
14
votes
2
answers
863
views
Must a space that is locally injective image of $\mathbb{R}^n$ be a manifold?
Suppose $X\subseteq\mathbb{R}^m$ s.t. for any $x\in X$ and any open $U\subseteq\mathbb{R}^m$ that contains $x$, there exists a smaller open set $V\subseteq U$ also containing $x$, so that $V\cap X$ is …
- 623
0
votes
Must a space that is locally injective image of $\mathbb{R}^n$ be a manifold?
I feel like this is true for $n=1$. Here is an outline. Suppose $X$ is Hausdorff and
$\{U\subseteq X\mid U\text{ is open and there exists a continuous bijection }f:\mathbb{R}\rightarrow U\}$
form a ba …
- 623