Higher-order orbifold Euler characteristics for compact Lie group actions
| dc.contributor.author | Gusein-Zade, Sabir Medgidovich | |
| dc.contributor.author | Luengo Velasco, Ignacio | |
| dc.contributor.author | Melle Hernández, Alejandro | |
| dc.date.accessioned | 2023-06-18T06:49:06Z | |
| dc.date.available | 2023-06-18T06:49:06Z | |
| dc.date.issued | 2015-12 | |
| dc.description.abstract | We generalize the notions of the orbifold Euler characteristic and of the higher-order orbifold Euler characteristics to spaces with actions of a compact Lie group using integration with respect to the Euler characteristic instead of the summation over finite sets. We show that the equation for the generating series of the kth-order orbifold Euler characteristics of the Cartesian products of the space with the wreath products actions proved by Tamanoi for finite group actions and by Farsi and Seaton for compact Lie group actions with finite isotropy subgroups holds in this case as well | |
| dc.description.department | Depto. de Álgebra, Geometría y Topología | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | Russian Foundation for Basic Research | |
| dc.description.sponsorship | President Grant for State Support of Leading Scientific Schools | |
| dc.description.sponsorship | Ministerio de ciencia y Tecnología (España) | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/35019 | |
| dc.identifier.doi | 10.1017/S030821051500027X | |
| dc.identifier.issn | 0308-2105 | |
| dc.identifier.officialurl | http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=10047657&fulltextType=RA&fileId=S030821051500027X | |
| dc.identifier.relatedurl | http://journals.cambridge.org/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/24292 | |
| dc.issue.number | 6 | |
| dc.journal.title | Proceedings of the Royal Society of Edinburgh: Section A Mathematics | |
| dc.language.iso | eng | |
| dc.page.final | 1222 | |
| dc.page.initial | 1215 | |
| dc.publisher | Cambridge University Press | |
| dc.relation.projectID | RFBR-13-01-00755 | |
| dc.relation.projectID | NSh-5138.2014.1 | |
| dc.relation.projectID | MTM2013-45710-C2-02-P | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 515.14 | |
| dc.subject.keyword | Lie group actions | |
| dc.subject.keyword | orbifold Euler characteristic | |
| dc.subject.keyword | wreath products | |
| dc.subject.keyword | generating series | |
| dc.subject.ucm | Topología | |
| dc.subject.unesco | 1210 Topología | |
| dc.title | Higher-order orbifold Euler characteristics for compact Lie group actions | |
| dc.type | journal article | |
| dc.volume.number | 145 | |
| dcterms.references | [1] M. Atiyah, G. Segal. On equivariant Euler characteristics. J. Geom. Phys. 6 (1989), no.4, 671–677. [2] V. Batyrev. Non-Archimedian integrals and stringy Euler numbers of log-Terminal pairs. J. Eur. Math. Soc. 1 (1999), 5–33. [3] J. Bryan, J. Fulman. Orbifold Euler characteristics and the number of commuting m-tuples in the symmetric groups. Ann. Comb. 2 (1998), no.1, 1–6. [4] C. Farsi, Ch. Seaton. Generalized orbifold Euler characteristics for general orbifolds and wreath products. Algebr. Geom. Topol. 11 (2011), no.1, 523–551 [5] S.M. Gusein-Zade. Integration with respect to the Euler characteristic and its applications. Russian Math. Surveys 65 (2010), no.3, 399–432. [6] S.M. Gusein-Zade, I. Luengo, A. Melle-Hernández. On the power structure over the Grothendieck ring of varieties and its applications. Proc. Steklov Inst. Math. 258 (2007), no.1, 53–64. [7] S.M. Gusein-Zade, I. Luengo, A. Melle-Hernández. Higher order generalized Euler characteristics and generating series. Preprint 2013, ArXiv math.AG/1303.5574. [8] F. Hirzebruch, Th. Höfer. On the Euler number of an orbifold. Math. Ann. 286 (1990), no.1-3, 255–260. [9] I.G. Macdonald. The Poincaré polynomial of a symmetric product, Proc. Cambridge Philos. Soc. 58 (1962), 563–568. [10] H. Tamanoi. Generalized orbifold Euler characteristic of symmetric products and equivariant Morava K-theory. Algebr. Geom. Topol. 1 (2001), 115–141. [11] O.Ya. Viro. Some integral calculus based on Euler characteristic. Topology and geometry: Rohlin Seminar, 127–138, Lecture Notes in Math., 1346, Springer, Berlin, 1988. [12] W.Wang, J. Zhou. Orbifold Hodge numbers of wreath product orbifolds. J. Geometry and Physics 38 (2001), 152–169. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 2e3a1e05-10b8-4ea5-9fcc-b53bbb0168ce | |
| relation.isAuthorOfPublication | c5f952f6-669f-4e3d-abc8-76d6ac56119b | |
| relation.isAuthorOfPublication.latestForDiscovery | 2e3a1e05-10b8-4ea5-9fcc-b53bbb0168ce |
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