  The paper mainly concerns the structure at infinity for complete gradient
shrinking Ricci solitons. It is shown that for such a soliton with bounded
curvature, if the round cylinder $\mathbb{R}\times \mathbb{S}^{n-1}/\Gamma$
occurs as a limit for a sequence of points going to infinity along an end, then
the end is asymptotic to the same round cylinder at infinity. The result is
then applied to obtain structural results at infinity for four dimensional
gradient shrinking Ricci solitons. It is previously known that such solitons
with scalar curvature approaching zero at infinity must be smoothly asymptotic
to a cone. For the case that the scalar curvature is bounded from below by a
positive constant, we conclude that along each end the soliton is asymptotic to
a quotient of $\mathbb{R}\times \mathbb{S}^{3}$ or converges to a quotient of
$\mathbb{R}^{2}\times \mathbb{S}^{2}$ along each integral curve of the gradient
vector field of the potential function.
