Normal triangulations in o-minimal structures
Elías Baro
Source: J. Symbolic Logic Volume 75, Issue 1
(2010), 275-288.
Abstract
Let ℛ be an o-minimal structure over a real closed field R. Given a simplicial complex K and some definable subsets S₁,..., Sl of its realization |K| in R we prove that there exist a subdivision K' of K and a definable triangulation φ':|K'|→ |K| of |K| partitioning S₁,...,Sl with φ' definably homotopic to id|K|. As an application of this result we obtain the semialgebraic Hauptvermutung.
First Page:
Show
Hide
Full-text: Access denied (no subscription
detected)
We're sorry, but we are unable to provide
you with the full text of this article because we are not able to identify
you as a subscriber.
If you have a personal subscription to
this journal, then please login. If you are already logged in, then you
may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.jsl/1264433921
Digital Object Identifier: doi:10.2178/jsl/1264433921
Zentralblatt MATH identifier: 05681304
Mathematical Reviews number (MathSciNet): MR2605894
References
E. Baro and M.Otero, On o-minimal homotopy groups, The Quarterly Journal of Mathematics, (2009), p. 15, doi:10.1093/qmath/hap011.
M. Coste, Unicité des triangulations semi-algébriques: validité sur un corps réel clos quelconque, et effectivité forte, Comptes Rendus de l'Académie des Sciences. Série I. Mathématique, vol. 312 (1991), no. 5, pp. 395--398.
Mathematical Reviews (MathSciNet): MR1096619
H. Delfs and M. Knebusch, Locally semialgebraic spaces, Lecture Notes in Mathematics, vol. 1173, Springer-Verlag, Berlin, 1985.
Mathematical Reviews (MathSciNet): MR819737
Joseph Johns, An open mapping theorem for o-minimal structures, Journal of Symbolic Logic, vol. 66 (2001), pp. 1817--1820.
Mathematical Reviews (MathSciNet): MR1877024
Zentralblatt MATH: 0993.03052
Digital Object Identifier: doi:10.2307/2694977
JSTOR: links.jstor.org
L. Lipshitz and Z. Robinson, Overconvergent real closed quantifier elimination, The Bulletin of the London Mathematical Society, vol. 38 (2006), no. 6, pp. 897--906.
Mathematical Reviews (MathSciNet): MR2285243
Zentralblatt MATH: 1116.03032
Digital Object Identifier: doi:10.1112/S0024609306018832
M. Shiota and M. Yokoi, Triangulations of subanalytic sets and locally subanalytic manifolds, Transactions of the American Mathematical Society, vol. 286 (1984), no. 2, pp. 727--750.
Mathematical Reviews (MathSciNet): MR760983
Zentralblatt MATH: 0527.57014
Digital Object Identifier: doi:10.2307/1999818
JSTOR: links.jstor.org
L. van den Dries, Tame topology and o-minimal structures, London Mathematical Society Lecture Note Series, vol. 248, Cambridge University Press, Cambridge, 1998.
Mathematical Reviews (MathSciNet): MR1633348
Zentralblatt MATH: 0953.03045
A. Woerheide, O-minimal homology, Ph.D. thesis, University of Illinois at Urbana-Champaign, 1996.
