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seen Jun 4 '13 at 11:52

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awarded  Curious
Dec
2
awarded  Nice Question
Dec
1
revised Eversion of the 6-sphere in 7-space
added 18 characters in body
Dec
1
asked Eversion of the 6-sphere in 7-space
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awarded  Yearling
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awarded  Enthusiast
Mar
15
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
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awarded  Nice Answer
Mar
12
awarded  Teacher
Mar
12
revised What are some examples of ingenious, unexpected constructions?
added 228 characters in body
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
6
revised Treating the Connected Sum (and other constructions) as a Push-out
added 1 characters in body
Mar
6
revised Treating the Connected Sum (and other constructions) as a Push-out
Made it more clear what I am looking for
Mar
5
comment 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
comment 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).
Mar
3
comment 3rd homotopy group of a compact Simple Lie Group
Just out of curiosity, why do we know $\pi_3(G)\cong\mathbb{Z}$? Is there a simple reason, like maybe it has $S^3$ or $S^2$ as universal cover or something?
Feb
25
revised Who defined the Inertia Group $I(M^n)\subset\Theta_n$ of a smooth manifold?
Added definition; deleted 5 characters in body