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If you're unfamiliar with the definition, for an oriented smooth manifold $M^n$ we define the inertia group $I(M)$ to be the set of (h-coboridsm classes of) homotopy spheres $\Sigma^n$ such that $M\#\Sigma$ is orientation-preserving diffeomorphic to $M$.

I'm trying to compile results into an expository Master's thesis on the subject, and it seems silly to not know the origin. Digging through old papers about the Inertia Group, I'm having a hard time finding the start of the trail. Many early papers refer to Tamura's "Sur les sommes connexes de certaines variétés différentiables" so I expect it to be close to the beginning, but I have been unable to find a copy of this paper.

I am aware of a few members here who are familiar with this theory, and maybe were even around when it started. Does anyone happen to know in which paper/book the Inertia Group originated?

edited Feb 25 2012 at 22:10

William

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I think a natural first guess would be Milnor. – Ryan Budney Feb 26 2012 at 4:28

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). – William Mar 5 2012 at 1:20

Who defined the Inertia Group $I(M^n)\subset\Theta_n$ of a smooth manifold?

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