Baro González, Elías and Otero, Margarita (2010) Locally definable homotopy. Annals of Pure and Applied Logic, 161 (4). pp. 488503. ISSN 01680072

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Abstract
In [E. Baro, M. Otero, On ominimal homotopy, Quart. J. Math. (2009) 15pp, in press (doi:10.1093/qmath/hap011)] ominimal homotopy was developed for the definable category, proving ominimal versions of the Hurewicz theorems and the Whitehead theorem. Here, we extend these results to the category of locally definable spaces, for which we introduce homology and homotopy functors. We also study the concept of connectedness in Vdefinable groups  which are examples of locally definable spaces. We show that the various concepts of connectedness associated to these groups, which have appeared in the literature, are nonequivalent.
Item Type:  Article 

Uncontrolled Keywords:  Ominimality; Locally definable space; Locally definable group; Connectedness; Ominimal homotopy; Homotopy functor; Homology functor 
Subjects:  Sciences > Mathematics > Logic, Symbolic and mathematical 
ID Code:  14472 
References:  E.Baro, Normal triangulations in ominimal structures, to appear in J. Symb. Log.,17pp. E.Baro, On ominimal homotopy. Dissertation submitted to apply for a Doctor degree in Mathematics, Universidad Autonoma de Madrid, 2009. E.Baro and M. Otero, On ominimal homotopy, 15pp., to appear in The Quarterly Journal of Mathematics 2009; doi: 10.1093/qmath/hap011 E.Baro and M.J.Edmundo, Corrigendum to Locally definable groups in ominimal structures, J. Algebra 320 (7) (2008), 30793080. A.Berarducci, M. Mamino and M. Otero, Higher homotopy of groups de_nable in ominimal structures, to appear in Israel J.Math., 12pp. A.Berarducci and M. Otero, oMinimal fundamental group, homology and manifolds, J. London Math. Soc. (2) (65) (2002), no. 2, 257270. H.Delfs and M. Knebusch, An introduction to locally semialgebraic spaces, Rocky Mountain J. Math. (14) (1984), no. 4, 945963. H.Delfs and M. Knebusch, Locally semialgebraic spaces, Lecture Notes in Mathematics, 1173, SpringerVerlag, Berlin, 1985. L. van den Dries, Tame topology and ominimal structures, London Mathematical Society Lecture Note Series, 248, Cambridge University Press, 1998. M.Edmundo, Locally de_nable groups in ominimal structures, J. Algebra 301 (1) (2006), 194223. M.Edmundo and P. Eleftheriou, The universal covering homomorphism in ominimal expansions of groups, Math. Logic Quart. 53 (6)(2007) 571582. M.Edmundo and M. Otero, Definably compact abelian groups, J. Math. Log. (4) (2004), no. 2, 163180. P. Eleftheriou, A semilinear group which is not affine, Annals of Pure and Applied Logic (156) (2008), 287289. E. Hrushovski, Y.Peterzil, A. Pillay, Groups, measures, and the NIP, J. Amer. Math.Soc. (21) (2008), no. 2, 563596. M. Otero and Y.Peterzil, Glinear sets and torsion points in definably compact groups, to appear in Archive Math. Logic. Y.Peterzil, Pillay's conjecture and its solutiona survey, for the proceedings of the Logic Colloquium, Wroclaw, 2007. Y.Peterzil and S. Starchenko, De_nable homomorphisms of abelian groups in ominimal structures, Ann. Pure Appl. Logic (101) (2000), no. 1, 127. A. Piekosz, Ominimal homotopy and generalized (co)homology, preprint, 2008. A.Woerheide, Ominimal homology, PhD Thesis, University of Illinois at UrbanaChampaign, 1996. 
Deposited On:  30 Jan 2012 08:31 
Last Modified:  06 Feb 2014 10:02 
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