  We use the terms, knot product and local move, as defined in the text of the
paper. Let $n$ be an integer$\geqq3$. Let $\mathcal S_n$ be the set of simple
spherical $n$-knots in $S^{n+2}$. Let $m$ be an integer$\geqq4$. We prove that
the map $j:\mathcal S_{2m}\to\mathcal S_{2m+4}$ is bijective, where
$j(K)=K\otimes$Hopf, and Hopf denotes the Hopf link.
  Let $J$ and $K$ be 1-links in $S^3$. Suppose that $J$ is obtained from $K$ by
a single pass-move, which is a local-move on 1-links. Let $k$ be a positive
integer. Let $P\otimes^kQ$ denote the knot product
$P\otimes\underbrace{Q\otimes...\otimes Q}_k$. We prove the following: The
$(4k+1)$-dimensional submanifold $J\otimes^k{\rm Hopf}$ $\subset S^{4k+3}$ is
obtained from $K\otimes^k{\rm Hopf}$ by a single $(2k+1,2k+1)$-pass-move, which
is a local-move on $(4k+1)$-submanifolds contained in $S^{4k+3}$. See the body
of the paper for the definitions of all local moves in this abstract.
  We prove the following: Let $a,b,a',b'$ and $k$ be positive integers. If the
$(a,b)$ torus link is pass-move equivalent to the $(a',b')$ torus link, then
the Brieskorn manifold $\Sigma(a,b,\underbrace{2,...,2}_{2k})$ is diffeomorphic
to $\Sigma(a',b',\underbrace{2,...,2}_{2k})$ as abstract manifolds.
  Let $J$ and $K$ be (not necessarily connected or spherical) 2-dimensional
closed oriented submanifolds in $S^4$. Suppose that $J$ is obtained from $K$ by
a single ribbon-move, which is a local-move on 2-dimensional submanifolds
contained in $S^4$. Let $k$ be an integer$\geq2$. We prove the following: The
$(4k+2)$-submanifold $J\otimes^k{\rm Hopf}$ $\subset S^{4k+4}$ is obtained from
$K\otimes^k{\rm Hopf}$ by a single $(2k+1,2k+2)$-pass-move, which is a
local-move on $(4k+2)$-dimensional submanifolds contained in $S^{4k+4}$.
