I am a beginner in surgery theory. I have started learning with ALGEBRAIC AND GEOMETRIC SURGERY by Andrew Ranicki.

On page 4 of the book he defines surgery :

**Denition 1.2** A surgery on an $m$-dimensional manifold $M^m$ is the procedure
of constructing a new $m$-dimensional manifold
$$M^{\prime m} =cl.(M\setminus S^n \times D^{m-n})\cup_{S^{n}\times S^{m-n-1}} D^{n+1}\times S^{m-n-1} $$

by cutting out $S^n \times D^{m-n}\subset M$ and replacing it by $D^{n+1}\times S^{m-n-1}$. The surgery **removes** $S^n \times D^{m-n}\subset M$ and **kills** the homotopy class $S^n \to M$ in $\pi_n (M)$.

**Question 1**: What is role of $S^{n}\times S^{m-n-1}$ as the subscript of $\cup$?

**Question 2**: I cannot understand the meaning of "it **kills** the homotopy class $S^n \to M$ in $\pi_n (M)$." Can anyone explain to me?

Thanks in advance.