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Oct 22, 2020 at 15:39 comment added Connor Malin @TimPerutz I have seen the term "inertia group" used by Weiss to refer to the subgroup of the exotic spheres which connect summing with does not change the diffeomorphism type of a specified manifold.
Apr 30, 2010 at 3:16 comment added Tim Perutz Igor, I guess the easy(ish) way out is to prove classification theorems up to connect sum with a homotopy-sphere. But I wonder how much we lose this way. Does connect summing with an exotic sphere always changes the manifold?
Apr 28, 2010 at 23:34 history answered Igor Belegradek CC BY-SA 2.5