Topology of Almost Complex Structures on Six-Manifolds
We study the space of (orthogonal) almost complex structures on closed six-dimensional manifolds as the space of sections of the twistor space for a given metric. For a connected six-manifold with vanishing first Betti number, we express the space of almost complex structures as a quotient of the sp...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2022 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2022
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/211811 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Topology of Almost Complex Structures on Six-Manifolds. Gustavo Granja and Aleksandar Milivojević. SIGMA 18 (2022), 093, 23 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862716766472372224 |
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| author | Granja, Gustavo Milivojević, Aleksandar |
| author_facet | Granja, Gustavo Milivojević, Aleksandar |
| citation_txt | Topology of Almost Complex Structures on Six-Manifolds. Gustavo Granja and Aleksandar Milivojević. SIGMA 18 (2022), 093, 23 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We study the space of (orthogonal) almost complex structures on closed six-dimensional manifolds as the space of sections of the twistor space for a given metric. For a connected six-manifold with vanishing first Betti number, we express the space of almost complex structures as a quotient of the space of sections of a seven-sphere bundle over the manifold by a circle action, and then use this description to compute the rational homotopy theoretic minimal model of the components that satisfy a certain Chern number condition. We further obtain a formula for the homological intersection number of two sections of the twistor space in terms of the Chern classes of the corresponding almost complex structures.
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| first_indexed | 2026-03-20T14:44:40Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211811 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-20T14:44:40Z |
| publishDate | 2022 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Granja, Gustavo Milivojević, Aleksandar 2026-01-12T10:15:12Z 2022 Topology of Almost Complex Structures on Six-Manifolds. Gustavo Granja and Aleksandar Milivojević. SIGMA 18 (2022), 093, 23 pages 1815-0659 2020 Mathematics Subject Classification: 32Q60; 53C27; 53C28; 55P62 arXiv:2207.12946 https://nasplib.isofts.kiev.ua/handle/123456789/211811 https://doi.org/10.3842/SIGMA.2022.093 We study the space of (orthogonal) almost complex structures on closed six-dimensional manifolds as the space of sections of the twistor space for a given metric. For a connected six-manifold with vanishing first Betti number, we express the space of almost complex structures as a quotient of the space of sections of a seven-sphere bundle over the manifold by a circle action, and then use this description to compute the rational homotopy theoretic minimal model of the components that satisfy a certain Chern number condition. We further obtain a formula for the homological intersection number of two sections of the twistor space in terms of the Chern classes of the corresponding almost complex structures. We thank Luis Fernandez and Scott Wilson for numerous illuminating discussions, and the referees for helpful comments. The first author was partially supported by FCT/Portugal through CAMGSD, IST-ID, projects UIDB/04459/2020 and UIDP/04459/2020. The second author would like to thank the Max Planck Institute for Mathematics in Bonn for its support, along with the Mittag-Leffler Institute in Djursholm for its hospitality during a visit to the “Higher algebraic structures in algebra, topology and geometry” program, where part of this work was carried out. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Topology of Almost Complex Structures on Six-Manifolds Article published earlier |
| spellingShingle | Topology of Almost Complex Structures on Six-Manifolds Granja, Gustavo Milivojević, Aleksandar |
| title | Topology of Almost Complex Structures on Six-Manifolds |
| title_full | Topology of Almost Complex Structures on Six-Manifolds |
| title_fullStr | Topology of Almost Complex Structures on Six-Manifolds |
| title_full_unstemmed | Topology of Almost Complex Structures on Six-Manifolds |
| title_short | Topology of Almost Complex Structures on Six-Manifolds |
| title_sort | topology of almost complex structures on six-manifolds |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211811 |
| work_keys_str_mv | AT granjagustavo topologyofalmostcomplexstructuresonsixmanifolds AT milivojevicaleksandar topologyofalmostcomplexstructuresonsixmanifolds |