Journal of the
Korean Mathematical Society JKMS

For 3-dimensional Bieberbach groups, we study the deformation spaces in the group of isometries of $\mathbb R^3$. First we calculate the discrete representation spaces and the automorphism groups. Then for each of these Bieberbach groups, we give complete descriptions of Teichm\"{u}ller spaces, Chabauty spaces, and moduli spaces.

Keywords: Bieberbach group, flat manifold, moduli space, Teichmuller spaces

MSC numbers: 32M17, 57N12, 32G15