An algebraic study of the Klein bottle
Denote by \(G\) the fundamental group of the Klein bottle. This article demonstrates, how to use the computer algebra system FriCAS to compute a resolution of \(\mathbb{Z}\) over the integer group ring of \(G\) and briefly presents the necessary mathematical background. From this resolution, the homology of the Klein bottle can be read off. Methods for manually deriving the same result have been explained in an earlier paper [\textit{L. Lambe}, J. Pure Appl. Algebra 84, No. 3, 311--329 (1993; Zbl 0766.55015)].
scientific article; zbMATH DE number 6675378
scientific article