A remark on the contactomorphism group of overtwisted contact spheres
| dc.contributor.author | Fernández Fuertes, Eduardo | |
| dc.contributor.author | Gironella, Fabio | |
| dc.date.accessioned | 2023-06-17T08:56:52Z | |
| dc.date.available | 2023-06-17T08:56:52Z | |
| dc.date.issued | 2020 | |
| dc.description.abstract | We show the existence of elements of infinite order in some homotopy groups of the contactomorphism group of overtwisted spheres. It follows in particular that the contactomorphism group of some high dimensional overtwisted spheres is not homotopically equivalent to a finite dimensional Lie group. | eng |
| dc.description.abstract | On prouve l’existence d’éléments d’ordre infini dans certains groupes d’homotopie du groupe des contactomorphismes des sphères vrillées. En particulier, il s’en suit que le groupe des contactomorphismes de certaines sphères vrillées n’est pas homotopiquement équivalent à un groupe de Lie de dimension finie. | fr |
| dc.description.department | Depto. de Álgebra, Geometría y Topología | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | FALSE | |
| dc.description.sponsorship | Ministerio de Ciencia e Innovación (MICINN) | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/63548 | |
| dc.identifier.doi | 10.5802/crmath.32 | |
| dc.identifier.issn | 1631-073X | |
| dc.identifier.officialurl | https://doi.org/10.5802/crmath.32 | |
| dc.identifier.relatedurl | https://comptes-rendus.academie-sciences.fr/mathematique/item/CRMATH_2020__358_2_189_0/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/7651 | |
| dc.issue.number | 2 | |
| dc.journal.title | Comptes rendus mathématique | |
| dc.language.iso | eng | |
| dc.page.final | 196 | |
| dc.page.initial | 189 | |
| dc.publisher | Académie des Sciences | |
| dc.relation.projectID | (MTM2016–79400– P; MTM2015–72876–EXP; SEV–2015–0554) | |
| dc.relation.projectID | NKFIH KKP 126683. | |
| dc.rights | Atribución 3.0 España | |
| dc.rights.accessRights | open access | |
| dc.rights.uri | https://creativecommons.org/licenses/by/3.0/es/ | |
| dc.subject.cdu | 514.7 | |
| dc.subject.keyword | Differential geometry | |
| dc.subject.keyword | Geometric group theory | |
| dc.subject.keyword | Geometría diferencial | |
| dc.subject.ucm | Matemáticas (Matemáticas) | |
| dc.subject.ucm | Geometría diferencial | |
| dc.subject.unesco | 12 Matemáticas | |
| dc.subject.unesco | 1204.04 Geometría Diferencial | |
| dc.title | A remark on the contactomorphism group of overtwisted contact spheres | |
| dc.type | journal article | |
| dc.volume.number | 358 | |
| dcterms.references | [1] Peter L. Antonelli; Dan Burghelea; Peter J. Kahn The non-finite homotopy type of some diffeomorphism groups, Topology, Volume 11 (1972), pp. 1-49 [2] Matthew Strom Borman; Yakov Eliashberg; Emmy Murphy Existence and classification of overtwisted contact structures in all dimensions, Acta Math., Volume 215 (2015) no. 2, pp. 281-361 [3] Raoul Bott The stable homotopy of the classical groups, Ann. Math., Volume 70 (1959), pp. 313-337 [4] Roger Casals; Ailsa Keating; Ivan Smith Symplectomorphisms of exotic discs, J. Éc. Polytech., Math., Volume 5 (2018), pp. 289-316 (With an appendix by Sylvain Courte) [5] Roger Casals; Álvaro del Pino; Francisco Presas Loose Engel structures, Compos. Math., Volume 156 (2020) no. 2, pp. 412-434 [6] Roger Casals; Francisco Presas A remark on the Reeb flow for spheres, J. Symplectic Geom., Volume 12 (2014) no. 4, pp. 657-671 [7] Roger Casals; Oldřich Spáčil Chern-Weil theory and the group of strict contactomorphisms, J. Topol. Anal., Volume 8 (2016) no. 1, pp. 59-87[8] Fan Ding; Hansjörg Geiges The diffeotopy group of S1×S2 via contact topology, Compos. Math., Volume 146 (2010) no. 4, pp. 1096-1112 [9] Katarzyna Dymara Legendrian knots in overtwisted contact structures on S3, Ann. Global Anal. Geom., Volume 19 (2001) no. 3, pp. 293-305 [10] Yakov Eliashberg Classification of overtwisted contact structures on 3-manifolds, Invent. Math., Volume 98 (1989) no. 3, pp. 623-637 [11] Yakov Eliashberg Contact 3-manifolds twenty years since J. Martinet’s work, Ann. Inst. Fourier, Volume 42 (1992) no. 1-2, pp. 165-192 [12] F. Thomas Farrell; Wu Chung Hsiang On the rational homotopy groups of the diffeomorphism groups of discs, spheres and aspherical manifolds, Algebraic and geometric topology (Stanford, Calif., 1976), Part 1 (Proceedings of Symposia in Pure Mathematics) Volume 32, American Mathematical Society, 1978, pp. 325-337 [13] Yves Félix; John Oprea; Daniel Tanré Algebraic models in geometry, Oxford Graduate Texts in Mathematics, Volume 17, Oxford University Press, 2008, xxii+460 pages [14] Hansjörg Geiges An introduction to contact topology, Cambridge Studies in Advanced Mathematics, Volume 109, Cambridge University Press, 2008, xvi+440 pages | [15] Hansjörg Geiges; Jesús Gonzalo Perez On the topology of the space of contact structures on torus bundles, Bull. Lond. Math. Soc., Volume 36 (2004) no. 5, pp. 640-646 | [16] Fabio Gironella Examples of contact mapping classes of infinite order in all dimensions (2018) (https://arxiv.org/abs/1809.07762, to appear in Math. Res. Lett.) [17] Fabio Gironella Examples of nontrivial contact mapping classes for overtwisted contact manifolds in all dimensions, Algebr. Geom. Topol., Volume 19 (2019) no. 3, pp. 1207-1227 [18] Emmanuel Giroux Sur les transformations de contact au-dessus des surfaces, Essays on geometry and related topics, Vol. 1, 2 (Monographies de l’Enseignement Mathématique) Volume 38, L’Enseignement Mathématique, 2001, pp. 329-350 [19] Emmanuel Giroux; Patrick Massot On the contact mapping class group of Legendrian circle bundles, Compos. Math., Volume 153 (2017) no. 2, pp. 294-312 | [20] Bruno Harris Some calculations of homotopy groups of symmetric spaces, Trans. Am. Math. Soc., Volume 106 (1963), pp. 174-184 [21] Allen E. Hatcher A proof of the Smale conjecture, Diff(S3)≃O(4), Ann. Math., Volume 117 (1983) no. 3, pp. 553-607 [22] Hideyuki Kachi Homotopy groups of symmetric spaces Γn, J. Fac. Sci., Shinshu Univ., Volume 13 (1978) no. 2, pp. 103-120 [23] Sergei Lanzat; Frol Zapolsky On the contact mapping class group of the contactization of the Am-Milnor fiber, Ann. Math. Qué., Volume 42 (2018) no. 1, pp. 79-94 [24] William S. Massey Obstructions to the existence of almost complex structures, Bull. Am. Math. Soc., Volume 67 (1961), pp. 559-564 [25] Patrick Massot Natural fibrations in contact topology, 2015 (Available at https://www.math.u-psud.fr/~pmassot/files/exposition/fibrations.pdf) [26] Patrick Massot; Klaus Niederkrüger Examples of non-trivial contact mapping classes in all dimensions, Int. Math. Res. Not., Volume 2016 (2016) no. 15, pp. 4784-4806 [27] Juno Mukai Remarks on homotopy groups of symmetric spaces, Math. J. Okayama Univ., Volume 32 (1990), pp. 159-164 [28] Thomas Vogel Non-loose unknots, overtwisted discs, and the contact mapping class group of S3, Geom. Funct. Anal., Volume 28 (2018) no. 1, pp. 228-288 [29] Michael Weiss; Bruce Williams Automorphisms of manifolds, Surveys on surgery theory, Vol. 2 (Annals of Mathematics Studies) Volume 149, Princeton University Press, 2001, pp. 165-220 | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 1f8860a9-0e65-435c-9295-bd1d136e100f | |
| relation.isAuthorOfPublication.latestForDiscovery | 1f8860a9-0e65-435c-9295-bd1d136e100f |
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