  Superconductivity in crystals without inversion symmetry has received
extensive attention due to its unconventional pairing and possible nontrivial
topological properties. Using first-principles calculations, we systemically
study the electronic structure of noncentrosymmetric superconductors
$A_2$Cr$_3$As$_3$ ($A$=Na, K, Rb and Cs). Topologically protected triply
degenerate points connected by one-dimensional arcs appear along the $C_{3}$
axis, coexisting with strong ferromagnetic (FM) fluctuations in the
non-superconducting state. Within random phase approximation, our calculations
show that strong enhancements of spin fluctuations are present in
K$_2$Cr$_3$As$_3$ and Rb$_2$Cr$_3$As$_3$, and are substantially reduced in
Na$_2$Cr$_3$As$_3$ and Cs$_2$Cr$_3$As$_3$. Symmetry analysis of spin-orbit
coupling $g_{k}$ suggests that the arc surface states might remain stable in
the superconducting state, giving rise to possible nontrivial topological
properties.
