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Results tagged with gt.geometric-topology
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user 238
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).
4
votes
Accepted
Notion of smoothness for set-valued functions
My idea is that if we want to compare $f(p)$ and $f(q)$ for nearby points $p$ and $q$, then we need to be able to put $f(p)$ and $f(q)$ into the same space. To do this, I'm going to assume that $M$ i …
4
votes
1
answer
545
views
Symmetries of the standard probability space
The standard probability space $(I, \mathcal B, \lambda)$ consists of the interval $I = [0,1]$, its Borel $\sigma$-algebra $\mathcal B := \mathcal B(I)$ and Lebesgue measure $\lambda$. In applications …
19
votes
3
answers
3k
views
When does the tangent bundle of a manifold admit a flat connection?
Let $M$ be a smooth manifold, and let $TM$ denote its tangent bundle. Under what conditions does $TM$ admit a flat connection $\omega$?
Edit: Formerly, I asked about a flat connection on the frame …