Szczepański, A. Intersection forms of almost-flat 4-manifolds. (English) Zbl 1398.57040 Arch. Math. 110, No. 5, 455-458 (2018). Summary: We calculate the intersection forms of all 4-dimensional almost-flat manifolds. MSC: 57R19 Algebraic topology on manifolds and differential topology 57M05 Fundamental group, presentations, free differential calculus 20H15 Other geometric groups, including crystallographic groups 22E25 Nilpotent and solvable Lie groups 53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.) Keywords:intersection form; almost-flat manifold; spin structure Software:GAP PDFBibTeX XMLCite \textit{A. Szczepański}, Arch. Math. 110, No. 5, 455--458 (2018; Zbl 1398.57040) Full Text: DOI arXiv References: [1] Ch. Bohr, On the signatures of even \[44\]-manifolds, Math. Proc. Cambridge 132 (2002), 453-469. · Zbl 1007.57017 [2] K. Dekimpe, Almost-Bieberbach Groups: Affine and Polynomial Structures, Lecture Notes in Mathematics, 1639, Springer, Berlin, 1996. · Zbl 0865.20001 [3] S. Donaldson, An application of gauge theory to four dimensional topology, J. Differential Geom. 18 (1983), 279-315. · Zbl 0507.57010 [4] S. Donaldson and P. Kronheimer, The Geometry of Four-Manifolds, Oxford University Press, Oxford, 1991. · Zbl 0904.57001 [5] The GAP Group, GAP - Groups, Algorithms, and Programming, Version 4.4.12, 2008, (http://www.gap-system.org). [6] A. Ga̧sior, N. Petrosyan,andA. Szczepański, Spin structures on almost-flat manifolds, Algebr. Geom. Topol. 16 (2016), 783-796. · Zbl 1338.53073 [7] J.-H. Kim, The \[\frac{10}{8}108\]-conjecture and equivariant \[e_C\] eC-invariants, Math. Ann. 329 (2004), 31-47. · Zbl 1070.57021 [8] R. Lutowski, N. Petrosyan, and A. Szczepański, Classification of spin structures on \[44\]-dimensional almost-flat manifold, accepted to Mathematika, arXiv:1701.03920. · Zbl 1390.53048 [9] J. W. Milnor and J. D. Stasheff, Charactersistic classes, Annals of Mathematics Studies, No. 76, Princeton University Press, Princeton, NJ and University of Tokyo Press, Tokyo, 1974. · Zbl 0298.57008 [10] B. Putrycz and A. Szczepański, Existence of spin structures on flat manifolds, Adv. Geometry 10 (2010), 323-332 · Zbl 1195.57049 · doi:10.1515/advgeom.2010.013 [11] J. Ratcliffe and S. Tschantz, Abelianization of space groups, Acta Crystallogr. 65 (2009), 18-27 · Zbl 1370.20043 · doi:10.1107/S0108767308036222 [12] A. Scorpan, The wild world of \[44\]-manifolds, American Mathematical Society, Providence, RI, 2005. · Zbl 1075.57001 [13] A. Szczepański, Geometry of crystallographic groups, In: Algebra and Discrete Mathematics, 4, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2012. · Zbl 1260.20070 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.