Skip to main content Accessibility help

Transfer methods for o-minimal topology

  • Alessandro Berarducci (a1) and Margarita Otero (a2)


Let M be an o-minimal expansion of an ordered field. Let φ be a formula in the language of ordered domains. In this note we establish some topological properties which are transferred from φ M to φ R and vice versa. Then, we apply these transfer results to give a new proof of a result of M. Edmundo—based on the work of A. Strzebonski—showing the existence of torsion points in any definably compact group defined in an o-minimal expansion of an ordered field.



Hide All
[1] Berarducci, A. and Otero, M., Some examples of transfer methods for o-minimal structures, The Proceedings of the Meeting “Spring Stage on Logic, Algebra and Geometry”, Caserta, Italy, 21–24 03 2000, preprint.
[2] Berarducci, A. and Otero, M., Intersection theory for o-minimal manifolds, Annals of Pure and Applied Logic, vol. 107 (2001), pp. 87119.
[3] Berarducci, A. and Otero, M., O-minimal fundamental group, homology and manifolds, Journal of the London Mathematical Society, vol. 65 (2002), pp. 257270.
[4] Brown, R., Elements of modern topology, McGraw-Hill, London, 1968.
[5] Brumfield, G. W., A Hopf fixed point theorem for semialgebraic maps, Real algebraic geometry, Proceedings of Rennes 1991, Lecture Notes in Mathematics, vol. 1524, Springer-Verlag, 1992.
[6] Delfs, H. and Knebusch, M., On the homology of algebraic varieties over real closed fields, Journal für die Reine und Angewandte Mathematik, vol. 335 (1982), pp. 122163.
[7] Edmundo, M. J., O-minimal cohomology and definably compact definable groups, preprint, 2000 (revised version 2001).
[8] Galewski, D. E. and Stern, R. J., Classification of simplicial triangulations of topological manifolds, Annals of Mathematics, vol. 111 (1980), pp. 134.
[9] Hocking, J. G. and Young, G. S., Topology, Dover Publications, New York, 1988.
[10] Johns, J., An open mapping for o-minimal structures, this Journal, vol. 66 (2001), pp. 18171820.
[11] Peterzil, Y. Otero, M. and Pillay, A., Groups and rings definable in o-minimal expansions of real closed fields, Bulletin of the London Mathematical Society, vol. 28 (1996), pp. 714.
[12] Milnor, J. W. and Stasheff, J. D., Characteristic classes, Annals of Mathematics Studies, Princeton University Press, Princeton, 1974.
[13] Peterzil, Y. and Steinhorn, C., Definable compactness and definable subgroups of o-minimal groups, Journal of the London Mathematical Society, vol. 59 (1999), pp. 769786.
[14] Pillay, A., On groups and fields definable in o-minimal structures. Journal of Pure and Applied Algebra, vol. 53 (1988), pp. 239255.
[15] Shiota, M., Geometry of subanalytic and semialgebraic sets, Progress in Mathematics, Birkhäuser, Boston, 1997.
[16] Strzebonski, A., Euler characteristic in semialgebraic and other o-minimal structures. Journal of Pure and Applied Algebra, vol. 96 (1994), pp. 173201.
[17] Thurston, W. P., Three-dimensional geometry and topology, Princeton University Press, 1997.
[18] van den Dries, L., Tame topology and o-minimal structures, London Mathematical Society Lecture Notes Series, vol. 248, Cambridge University Press, 1998.
[19] Vick, J. W., Homology theory, Springer-Verlag, 1994.
[20] Woerheide, A., O-minimal homology, Ph.D. thesis , University of Illinois at Urbana-Champaign, 1996.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed