A knot K in the 3-sphere is said to have Property nR if, whenever K is a
component of an n-component link L and some integral surgery on L produces the
connected sum of n copies of S^1 x S^2, there is a sequence of handle slides on
L that converts L into a 0-framed unlink. The Generalized Property R Conjecture
is that all knots have Property nR for all n.