The spin of domain wall

Question

Suppose we have 2-d system in which there is spontaneous symmetry breaking $Z_{2} \to \hat{I}$. Corresponding homotopy group is $Z$, and defects called domain walls arise. How to determine their spin (for example, instantons carry zero spin, while skyrmions may be fermions as well as bosons)?

Comments

Can you explain a bit more: of what is the homotopy group $\mathbb Z$, and how is this related to symmetry breaking/domain walls?