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Results tagged with gt.geometric-topology
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user 36688
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).
6
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0
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209
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A tangential fixed point property for manifolds embedded in Euclidean spaces
Assume that $M$ is a compact orientable manifold which is embedded in some Euclidean space $\mathbb{R}^{N}$
We say that $M\subset \mathbb{R}^{N}$ has the tangential fixed point property if for eve …
- 356
4
votes
2
answers
372
views
Maps between grassmannians with inclusion property
Edit: According to the comment of L. Spice I changed the inclusion sign to the subset sign.
Is there a continuous map $f:\mathbb{C}P^3 \to \textrm{Gr}_{\mathbb{C}}(2,4)$ with $x\subset f(x)$? What ab …
- 356
4
votes
0
answers
352
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A generalized ellipse
We know that an ellipse is the locus of all point $z$ in the plane with $$|z-a|+|z-b|=\lambda$$
where $a,b$ are two given points in the plane and $\lambda$ is a constant.
Now we consider the follo …
- 356
5
votes
1
answer
372
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A possible characterization of sphere or projective space
Is there a compact Riemanian manifold $M$ not diffeomorphic to sphere or real or complex or quaternion projective space which admit a diffeomorphism $f$ with the property that $$\forall x \in M, \qu …
- 356
1
vote
Are there some other notions of "curvature" which measure how space curves?
Let $\gamma$ be a regular curve in the plan. we can assign various quantities $\tilde{\kappa}$ to $\gamma$ as follows: every quantity which is independent of parametrization, for example $\gamma^{(n) …
1
vote
Are there some other notions of "curvature" which measure how space curves?
Assume that $M$ is a Riemannian manifold which is equipped with symplectic structure $\omega$.
Inspired by the definition of "Scalar curvature", one can define the quantity $tr_{\omega} Ric$ where $ …
2
votes
Generalization of winding number to higher dimensions
In your question you mentioned the word "Fredholm index".
So I would like to say that in the circle case there are two different interpretations of Fredholm index of certain lin …
- 356
2
votes
0
answers
82
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Is isoperimetric hypersurface unique up to homeomorphism?
Is there a Riemannian structure on $\mathbb{R}^n $with two non homeomorphic compact hypersurfaces $M,N$ such that both satisfy the isoperimetric inequality. I precisely meanthe following:
$$\el …
- 356