by Ilka Agricola and Thomas Friedrich
We thank all colleagues that pointed out mistakes in the German and English edition of our book.
Mistakes of the English edition known so far:
p. 145, proof of Thm 23, l. 8: The last case discussed is equivalent to (4), not (2), which makes the remaining part of the text more understandable, of course. Instead of the suggested replacement, one can argue as follows: Geometrically, the lattice described has to be rhombic (all edges are equally long) - in particular, the diagonals intersect diagonally and cannot be of equal lengths (otherwise, one would have a right angle in the rhombus, i.e. case (3)). Nows start with any long diagonal and its endpoints, and complete it by taking two short diagonals and one long diagonal from adjacent rhombi to a full rectangle; a picture shows that there is precisely one lattice point inside the rectangle, namely, its center. Thus, one is back to (4).
p. 206, first picture: The picture of the stereographic projection is misleading. The projection is done onto the plane through the equator, not onto the plane tangent to the south pole.