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Eversion of the 6-sphere in 7-space
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comment |
What are some examples of ingenious, unexpected constructions?
I think they are non-intuitive simply because I wouldn't expect them to happen. Maybe that's just me. |
Mar
13 |
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What are some examples of ingenious, unexpected constructions?
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Mar
12 |
answered | What are some examples of ingenious, unexpected constructions? |
Mar
7 |
comment |
Treating the Connected Sum (and other constructions) as a Push-out
Yes, that is the "with collars" construction I am thinking about (equivalently you could take $S^{n-1} \times (0,1)$) Do you think I should edit the OP to make that more explicit? |
Mar
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Treating the Connected Sum (and other constructions) as a Push-out
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Mar
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revised |
Treating the Connected Sum (and other constructions) as a Push-out
Made it more clear what I am looking for |
Mar
5 |
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Treating the Connected Sum (and other constructions) as a Push-out
@Daniel No, that is not the question I am interested in. I am more interested in the cases where the topological pushout is actually a smooth pushout. Does this not happen even when the construction includes collars? |
Mar
5 |
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Treating the Connected Sum (and other constructions) as a Push-out
This is not an example of the construction I am considering. I am aware that a collar is needed in order to induce a smooth structure on an open overlap. I am not asserting that every topological pushout is a Smooth pushout, I am looking for a reference in the cases where it is. |
Mar
5 |
asked | Treating the Connected Sum (and other constructions) as a Push-out |
Mar
5 |
comment |
Who defined the Inertia Group $I(M^n)\subset\Theta_n$ of a smooth manifold?
Update: My supervisor found me a copy of Tamura's paper! In one corollary at the end he has a diffeomorphism between a $7$-manifold and its connected sum with a non-trivial Milnor sphere, but nowhere in the paper does he use "inertial" or "$I(M)$" (or French equivalents). I haven't managed to find the definition in anything by Milnor yet either (he does use "$I(M)$" in "Differentiable Manifolds which are homotopy spheres," but here it refers to the index aka signature). |