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visits | member for | 2 years, 11 months |
seen | Jun 4 '13 at 11:52 | |
stats | profile views | 206 |
Jul 2 |
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 |
Sep 17 |
awarded | Yearling |
Mar 16 |
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 13 |
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 |