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On the o-minimal LS-category

Baro González, Elías (2011) On the o-minimal LS-category. Israel Journal of mathematics, 185 (1). pp. 61-76. ISSN 0021-2172

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Abstract

We introduce the o-minimal LS-category of definable sets in o-minimal expansions of ordered fields and we establish a relation with the semialgebraic and the classical one. We also study the o-minimal LS-category of definable groups. Along the way, we show that two definably connected definably compact definable groups G and H are definable homotopy equivalent if and only if L(G) and L(H) are homotopy equivalent, where L is the functor which associates to each definable group its corresponding Lie group via Pillay's conjecture.


Item Type:Article
Uncontrolled Keywords:O-minimality; LS-category; Definable groups; Homotopy equivalences
Subjects:Sciences > Mathematics > Algebra
ID Code:14499
References:

[1] E.Baro, Normal triangulations in o-minimal structures, J. Symb. Log., 15pp. (in press).

[2] E.Baro and M. Otero, On o-minimal homotopy groups, Quart. J. Math., (2009), in press (doi: 10.1093/qmath/hap011), 15pp.

[3] A.Berarducci, O-minimal spectra, in_nitesimal subgroups and cohomology, J. Symb. Log. 72 (2007), no. 4, 1177-1193.

[4] A.Berarducci and M. Mamino, Equivariant homotopy of de_nable groups, e-print, arXiv:0905.1069, 2009.

[5] A.Berarducci, M. Mamino and M. Otero, Higher homotopy of groups de_nable in o-minimal structures, Israel J. Math, 13pp. (in press).

[6] A.Berarducci, M. Otero, Y.Peterzil, A. Pillay, A descending chain condition for groups denable in o-minimal structures, Annals of Pure and Applied Logic 134 (2005) 303-313.

[7] A.Borel, Sous-groupes commutatifs et torsion des groupes de Lie compacts connexes, Tohoku Math. J. (2) 13 (1961) 216-240.

[8] O. Cornea, G. Lupton, J. Oprea, D.Tanr_e, Lusternik-Schnirelmann Category, American Mathematical Society, Providence, 2003.

[9] H.Delfs and M. Knebusch, Locally semialgebraic spaces, Lecture Notes in Mathematics, 1173, Springer-Verlag, Berlin, 1985.

[10] L. van den Dries, Tame topology and o-minimal structures, London Mathematical Society Lecture Note Series, 248, Cambridge University Press, 1998.

[11] M.Edmundo and M. Otero, Definably compact abelian groups, J. Math. Log. 4 (2004), no. 2, 163-180.

[12] E. Hrushovski, Y.Peterzil and A. Pillay, Groups, measures, and the NIP, J.Amer. Math. Soc., 21 (2008), no.2, 563-596.

[13] E. Hrushovski, Y.Peterzil and A. Pillay, On central extensions and definably compact groups in o-minimal structures, e-print, arXiv:0811.0089, 2008.

[14] Y.Peterzil and C. Steinhorn, Definable compactness and definable subgroups of o-minimal groups, J. London Math. Soc., vol. 59 (1999), no. 3, pp. 769-786.

[15] A. Pillay, Type-definability, compact Lie groups, and o-minimality, J. Math. Logic 4 (2004), 147-162.

[16] N. Steenrod, The Topology of Fibre Bundles, Princeton Mathematical Series, vol. 14. Princeton University Press, Princeton, N. J., 1951.

Deposited On:01 Feb 2012 15:30
Last Modified:06 Feb 2014 10:03

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