- The repetition of "and" in the quotation is a transcription error, and not in the original!
- The "killing" terminology in surgery is the manifold version of the killing of homotopy classes by attaching cells: for any space $X$ the space $Y=X\cup_fD^{n+1}$ obtained from $X$ by attaching an $(n+1)$-cell along a map $f:S^n \to X$ has $n$th homotopy group $\pi_n(Y)=\pi_n(X)/\langle [f] \rangle$, so the group morphism $\pi_n(X) \to \pi_n(Y)$ induced by the inclusion $X \to Y$ sends the homotopy class $[f] \in \pi_n(X)$ to $0 \in \pi_n(Y)$, i.e. "kills" it. The killing of homotopy classes by attaching cells is a method for constructing new spaces with particular homotopy theoretic properties (e.g. the Eilenberg-MacLane spaces $K(\pi,n)$) which was developed in the 1940's and 1950's, notably by Cartan and Serre.
- Milnor's classic 1961 paper "A procedure for killing homotopy groups of differenntiable manifolds" is available from http://www.maths.ed.ac.uk/~aar/papers/milnorsurg.pdf
- I recommend using Google to search for surgery references (such as 3.)
Andrew Ranicki
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