Questions tagged [shape-theory]

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Topological Shape Operator More Sensitive than Inverse Limits

This is a very general sort of question, and the use of the phrase 'shape operator' is a bit sloppy since there is already an established "shape theory." But what I have are topological spaces that ...
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0answers
92 views

Fixed point shape property

Question: Provide (or prove that it's not possible) a metric compact space which has the fixed point property but not the fixed point shape property. Here is the definition of f.p.s.p.("map" means ...
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0answers
160 views

Inverse limit in shape theory

Is the shape theory of Hausdorff compact spaces complete with respect to the inverse limit operation?--complete means that for every inverse system of Hausdorff compact spaces, and the shape morphisms ...
11
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0answers
156 views

Classes for which the Spectrum determines a Convex Shape

Given a planar domain $\Omega \subset \Bbb{R}^2$ bounded and open we can associate to it the spectrum of the Laplace operator with Dirichlet boundary condition. It is known that there are planar ...
2
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1answer
285 views

Optimal, conformal diffeomorphisms between two surfaces in 3D

Let $S_1$ and $S_2$ be two smooth, closed surfaces embedded in $\mathbb{R}^3$. Q. Is there a natural definition of the optimal, conformal diffeomorphism between $S_1$ and $S_2$? I am imagining $...
1
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1answer
479 views

Packing a closed 3D surface with non-overlapping spheres starting with the largest possible one and then working the way down

Let's say, I have a closed 3D surface (say, the surface of a pebble). I want to pack it with spheres, but starting with the largest possible sphere, then the next largest possible non-overlapping ...
31
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3answers
2k views

For which spaces is homology (or cohomology) determined by the Eilenberg-Steenrod axioms

This is a spinoff of Can anyone give me a good example of two interestingly different ordinary cohomology theories? . By an ordinary homology theory, I mean a functor on topological spaces which ...