Topological Invariants of Principal G-Bundles with Singularities
principal G-bundle with singularities is a principal bundle π: P¯ → M with structure group G¯ which reduces to a subgroup G ⊂ G¯ on the set M \ Σ, where M is an n-dimensional compact manifold and Σ ⊂ M is a k-dimensional submanifold. For example, a vector field on an n-dimensional Riemannian manifol...
- Autores:
- Tipo de recurso:
- Fecha de publicación:
- 2018
- Institución:
- Universidad Tecnológica de Bolívar
- Repositorio:
- Repositorio Institucional UTB
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.utb.edu.co:20.500.12585/8879
- Acceso en línea:
- https://hdl.handle.net/20.500.12585/8879
- Palabra clave:
- G-structure
Obstruction
Principal bundle with singularities
Singularity of G-structure
- Rights
- restrictedAccess
- License
- http://creativecommons.org/licenses/by-nc-nd/4.0/
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Topological Invariants of Principal G-Bundles with Singularities |
| title |
Topological Invariants of Principal G-Bundles with Singularities |
| spellingShingle |
Topological Invariants of Principal G-Bundles with Singularities G-structure Obstruction Principal bundle with singularities Singularity of G-structure |
| title_short |
Topological Invariants of Principal G-Bundles with Singularities |
| title_full |
Topological Invariants of Principal G-Bundles with Singularities |
| title_fullStr |
Topological Invariants of Principal G-Bundles with Singularities |
| title_full_unstemmed |
Topological Invariants of Principal G-Bundles with Singularities |
| title_sort |
Topological Invariants of Principal G-Bundles with Singularities |
| dc.subject.keywords.none.fl_str_mv |
G-structure Obstruction Principal bundle with singularities Singularity of G-structure |
| topic |
G-structure Obstruction Principal bundle with singularities Singularity of G-structure |
| description |
principal G-bundle with singularities is a principal bundle π: P¯ → M with structure group G¯ which reduces to a subgroup G ⊂ G¯ on the set M \ Σ, where M is an n-dimensional compact manifold and Σ ⊂ M is a k-dimensional submanifold. For example, a vector field on an n-dimensional Riemannian manifold M defines reduction of the orthonormal frame bundle of M to the subgroup O(n − 1) ⊂ O(n) on the set M \ Σ, where Σ is the set of zeros of this vector field. The aim of this paper is to construct topological invariants of principal bundles with singularities. To do this we apply the obstruction theory to the sectionM → P¯ /Gcorresponding to the reduction and obtain the topological invariant as a class in Hn−k(M,M \ Σ; πn−k−1(G¯ /G)). We study the properties of this invariants and, in particular, consider cases k = 0 y k = n − 1. © 2018, Pleiades Publishing, Ltd. |
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2018 |
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2018 |
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2020-03-26T16:32:33Z |
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2020-03-26T16:32:33Z |
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Artículo |
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Lobachevskii Journal of Mathematics; Vol. 39, Núm. 5; pp. 623-633 |
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19950802 |
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https://hdl.handle.net/20.500.12585/8879 |
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10.1134/S1995080218050013 |
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Universidad Tecnológica de Bolívar |
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Repositorio UTB |
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57076963500 6507151476 |
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Lobachevskii Journal of Mathematics; Vol. 39, Núm. 5; pp. 623-633 19950802 10.1134/S1995080218050013 Universidad Tecnológica de Bolívar Repositorio UTB 57076963500 6507151476 |
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https://hdl.handle.net/20.500.12585/8879 |
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eng |
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eng |
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Pleiades Publishing |
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Pleiades Publishing |
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2020-03-26T16:32:33Z2020-03-26T16:32:33Z2018Lobachevskii Journal of Mathematics; Vol. 39, Núm. 5; pp. 623-63319950802https://hdl.handle.net/20.500.12585/887910.1134/S1995080218050013Universidad Tecnológica de BolívarRepositorio UTB570769635006507151476principal G-bundle with singularities is a principal bundle π: P¯ → M with structure group G¯ which reduces to a subgroup G ⊂ G¯ on the set M \ Σ, where M is an n-dimensional compact manifold and Σ ⊂ M is a k-dimensional submanifold. For example, a vector field on an n-dimensional Riemannian manifold M defines reduction of the orthonormal frame bundle of M to the subgroup O(n − 1) ⊂ O(n) on the set M \ Σ, where Σ is the set of zeros of this vector field. The aim of this paper is to construct topological invariants of principal bundles with singularities. To do this we apply the obstruction theory to the sectionM → P¯ /Gcorresponding to the reduction and obtain the topological invariant as a class in Hn−k(M,M \ Σ; πn−k−1(G¯ /G)). We study the properties of this invariants and, in particular, consider cases k = 0 y k = n − 1. © 2018, Pleiades Publishing, Ltd.Acknowledgement. This investigation was supported by Vicerrectoría de Investigaciones and the Faculty of Sciences of Universidad de los Andes.Recurso electrónicoapplication/pdfengPleiades Publishinghttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/restrictedAccessAtribución-NoComercial 4.0 Internacionalhttp://purl.org/coar/access_right/c_16echttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85049590504&doi=10.1134%2fS1995080218050013&partnerID=40&md5=bce3246b966ea8a5b62709e9331e2607Topological Invariants of Principal G-Bundles with Singularitiesinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArtículohttp://purl.org/coar/version/c_970fb48d4fbd8a85http://purl.org/coar/resource_type/c_2df8fbb1G-structureObstructionPrincipal bundle with singularitiesSingularity of G-structureArias Amaya, FabiánMalakhaltsev M.Alekseevskij, D.V., Vinogradov, A.M., Lychagin, V.V., (1991) Geometry I. Basic Ideas and Concepts of Differential Geometry, Vol. 28 of Encyclopaedia of Mathematical Sciences, p. 255. , Springer, BerlinKobayashi, S., Nomizu, K., (1963) Foundations of Differential Geometry, 1. , Interscience, New York, LondonMolino, P., Théorie des G-structures: le problème d’equivalence (1977) Lect. NotesMath., 588, p. 1Sternberg, S., (1983) Lectures on Differential Geometry, , Chelsea, New YorkIvey, T.A., Landsberg, J.M., (2016) Cartan for the Beginners: Differential Geometry viaMoving Frames and Exterior Differential Systems, Vol. 175 of Graduate Studies in Mathematics, , AMS, ProvidenceMontgomery, R., (2002) A Tour of Subriemannian Geometries, Their Geodesics and Applications, Vol. 91 of Math. Surveys and Monographs, , AMS, ProvidenceBott, R.W., Tu, L.W., (1982) Differential forms in Algebraic Topology, Vol. 82 of Graduate Texts in Mathematics, , Springer, New York, Heidelberg, BerlinMilnor, J.W., Stasheff, J.D., (2005) Characteristic Classes, Vol. 32 of Texts and Readings in Mathematics, , Hindustan Book Agency, New DelhiKamber, F.W., Tondeur, P., (1975) Foliated Bundles and Characteristic Classes, , Springer-Verlag, BerlinZhitomirskii, M., (1992) Typical Singularities of Differential 1-forms and Pfaffian Equations, Vol. 113 of Translation of Mathematical Monographs, , AMS, ProvidenceMartinet, J., Sur les singularités des formes différentielles (1970) Ann. Inst. Fourier.Grenoble, 20, pp. 95-178Malakhaltsev, M., A bundle of local Hamiltonians on a symplectic manifold with Martinet singularities (2004) Russ. Math. (Iz. VUZ), 48 (11), pp. 41-47Malakhaltsev, M., Differential complex associated to closed differential forms of nonconstant rank (2006) Lobachevskii J.Math., 23, pp. 183-192Arteaga, J., Malakhalsev, M., Trejos, A., Isometry group and geodesics of theWagner lift of a Riemannian metric on two-dimensional manifold (2012) Lobachevskii J.Math., 33, pp. 293-311Arteaga, J.R., Malakhaltsev, M., Symmetries of sub-Riemannian surfaces (2011) J. Geom. Phys., 61, pp. 290-308Arias, F.A., Arteaga, J.R., Malakhaltsev, M., 3-webs with singularities (2016) Lobachevskii J.Math., 37, pp. 1-20Arias, F.A., Malakhaltsev, M., A generalization of the Gauss–Bonnet–Hopf–Poincaréformula for sections and branched sections of bundles (2017) J. Geom. Phys, 121, pp. 108-122Mukherjee, A., (2015) Differential Topology, Vol. 72 of Texts and Readings in Mathematics, , Birkhäuser, BaselDubrovin, B.A., Fomenko, A.T., Novikov, S.P., (1990) Modern Geometry—Methods and Applications, Part III: Introduction to Homology Theory, Vol. 124 of Graduate Texts in Mathematics, , Springer, New York etcJakubszyk, B., Zhitomirskii, M., Local reduction theorems and invariants for singular contact structures (2001) Ann. Inst. Fourier, 51, pp. 237-295Steenrod, N., (1951) The Topology of Fibre Bundles, , Princeton Univ. Press, Princetonhttp://purl.org/coar/resource_type/c_6501THUMBNAILMiniProdInv.pngMiniProdInv.pngimage/png23941https://repositorio.utb.edu.co/bitstream/20.500.12585/8879/1/MiniProdInv.png0cb0f101a8d16897fb46fc914d3d7043MD5120.500.12585/8879oai:repositorio.utb.edu.co:20.500.12585/88792023-05-25 11:41:51.409Repositorio Institucional UTBrepositorioutb@utb.edu.co |