# Comparison between $U(1)$, $SU(N)$ and $SO(N)$ instantons

I am interested in knowing the details of the comparison between $U(1)$, $SU(N)$ and $SO(N)$ instantons for their gauge theories in 4 spacetime dimensions., in terms of:

1. Chern class (1st, 2nd), and

2. Pontryagin class

3. And their normalization and mapping between the instanton numbers. For example, the instanton number 1 in $U(1)$ gauge theory may map to the instanton number 2 in $SU(2)$ gauge theory, etc.