On the o-minimal LS-category
| dc.contributor.author | Baro González, Elías | |
| dc.date.accessioned | 2023-06-20T00:08:02Z | |
| dc.date.available | 2023-06-20T00:08:02Z | |
| dc.date.issued | 2011 | |
| dc.description.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. | |
| dc.description.department | Depto. de Álgebra, Geometría y Topología | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | Ministerio de Educación y Cultura (España) | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/14499 | |
| dc.identifier.citation | Baro E. on the o-minimal LS-category. Isr J Math 2011;185:61–76. https://doi.org/10.1007/s11856-011-0101-x. | |
| dc.identifier.doi | 10.1007/s11856-011-0101-x | |
| dc.identifier.issn | 0021-2172 | |
| dc.identifier.officialurl | https://doi.org/10.1007/s11856-011-0101-x. | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/42050 | |
| dc.issue.number | 1 | |
| dc.journal.title | Israel Journal of mathematics | |
| dc.language.iso | eng | |
| dc.page.final | 76 | |
| dc.page.initial | 61 | |
| dc.publisher | Springer Verlag | |
| dc.relation.projectID | info:eu-repo/grantAgreement/MICINN//MTM2008-00272/ES/GEOMETRIA REAL/ | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 512 | |
| dc.subject.keyword | O-minimality | |
| dc.subject.keyword | LS-category | |
| dc.subject.keyword | Definable groups | |
| dc.subject.keyword | Homotopy equivalences | |
| dc.subject.ucm | Álgebra | |
| dc.subject.unesco | 1201 Álgebra | |
| dc.title | On the o-minimal LS-category | |
| dc.type | journal article | |
| dc.volume.number | 185 | |
| dcterms.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. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 8695b08a-762f-4ef9-ad24-b6fe687ab7cd | |
| relation.isAuthorOfPublication.latestForDiscovery | 8695b08a-762f-4ef9-ad24-b6fe687ab7cd |
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