Skip to main content
SpringerLink
Log in

Intersection forms of almost-flat 4-manifolds

  • Published:
Archiv der Mathematik Aims and scope Submit manuscript

Abstract

We calculate intersection forms of all 4-dimensional almost-flat manifolds.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Ch. Bohr, On the signatures of even \(4\)-manifolds, Math. Proc. Cambridge 132 (2002), 453–469.

  2. K. Dekimpe, Almost-Bieberbach Groups: Affine and Polynomial Structures, Lecture Notes in Mathematics, 1639, Springer, Berlin, 1996.

  3. S. Donaldson, An application of gauge theory to four dimensional topology, J. Differential Geom. 18 (1983), 279–315.

  4. S. Donaldson and P. Kronheimer, The Geometry of Four-Manifolds, Oxford University Press, Oxford, 1991.

  5. The GAP Group, GAP – Groups, Algorithms, and Programming, Version 4.4.12, 2008, (http://www.gap-system.org).

  6. A. Ga̧sior, N. Petrosyan, and A. Szczepański, Spin structures on almost-flat manifolds, Algebr. Geom. Topol. 16 (2016), 783–796.

  7. J.-H. Kim, The \(\frac{10}{8}\)-conjecture and equivariant \(e_{C}\)-invariants, Math. Ann. 329 (2004), 31–47.

  8. R. Lutowski, N. Petrosyan, and A. Szczepański, Classification of spin structures on \(4\)-dimensional almost-flat manifold, accepted to Mathematika, arXiv:1701.03920.

  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.

  10. B. Putrycz and A. Szczepański, Existence of spin structures on flat manifolds, Adv. Geometry 10 (2010), 323–332

    Article  MathSciNet  MATH  Google Scholar 

  11. J. Ratcliffe and S. Tschantz, Abelianization of space groups, Acta Crystallogr. 65 (2009), 18–27

    Article  MathSciNet  MATH  Google Scholar 

  12. A. Scorpan, The wild world of \(4\)-manifolds, American Mathematical Society, Providence, RI, 2005.

    MATH  Google Scholar 

  13. A. Szczepański, Geometry of crystallographic groups, In: Algebra and Discrete Mathematics, 4, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2012.

Download references

Acknowledgements

We would like to thank K. Dekimpe, R. Lutowski, M. Mroczkowski and N. Petrosyan for some useful comments.

Author information

Authors and Affiliations

  1. Institute of Mathematics, University of Gdańsk, ul. Wita Stwosza 57, 80-952, Gdańsk, Poland

    A. Szczepański

Authors
  1. A. Szczepański
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. Szczepański.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Szczepański, A. Intersection forms of almost-flat 4-manifolds. Arch. Math. 110, 455–458 (2018). https://doi.org/10.1007/s00013-017-1148-7

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00013-017-1148-7

Mathematics Subject Classification

Keywords

Search

Navigation