On the fundamental group calculation associated to reverse-engineering an exotic CP ^2 #3 \overline{CP }^2 and CP ^2 #2 \overline{CP }^2

Abstract

I provide a detailed exposition of the fundamental group calculations in the ``reverse engineering" construction of an exotic $\CP ^2\#3\overline{\CP }^2$ and of an exotic $\CP ^2\#2\overline{\CP }^2$.