On the characterization of rational homotopy types and Chern classes of closed almost complex manifolds
We give an exposition of Sullivan’s theorem on realizing rational homotopy types by closed smooth manifolds, including a discussion of the necessary rational homotopy and surgery theory, adapted to the realization problem for almost complex manifolds: namely, we give a characterization of the possib...
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| Format: | Article |
| Language: | English |
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De Gruyter
2022-05-01
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| Series: | Complex Manifolds |
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| Online Access: | https://doi.org/10.1515/coma-2021-0133 |
| _version_ | 1811171893806366720 |
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| author | Milivojević Aleksandar |
| author_facet | Milivojević Aleksandar |
| author_sort | Milivojević Aleksandar |
| collection | DOAJ |
| description | We give an exposition of Sullivan’s theorem on realizing rational homotopy types by closed smooth manifolds, including a discussion of the necessary rational homotopy and surgery theory, adapted to the realization problem for almost complex manifolds: namely, we give a characterization of the possible simply connected rational homotopy types, along with a choice of rational Chern classes and fundamental class, realized by simply connected closed almost complex manifolds in real dimensions six and greater. As a consequence, beyond demonstrating that rational homotopy types of closed almost complex manifolds are plenty, we observe that the realizability of a simply connected rational homotopy type by a simply connected closed almost complex manifold depends only on its cohomology ring. We conclude with some computations and examples. |
| first_indexed | 2024-04-10T17:22:54Z |
| format | Article |
| id | doaj.art-942cf9ec7f1d42efa80993a6f1a4e902 |
| institution | Directory Open Access Journal |
| issn | 2300-7443 |
| language | English |
| last_indexed | 2024-04-10T17:22:54Z |
| publishDate | 2022-05-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Complex Manifolds |
| spelling | doaj.art-942cf9ec7f1d42efa80993a6f1a4e9022023-02-05T08:30:37ZengDe GruyterComplex Manifolds2300-74432022-05-019113816910.1515/coma-2021-0133On the characterization of rational homotopy types and Chern classes of closed almost complex manifoldsMilivojević Aleksandar0Max Planck Institute for Mathematics, Vivatsgasse 7, 53111BonnWe give an exposition of Sullivan’s theorem on realizing rational homotopy types by closed smooth manifolds, including a discussion of the necessary rational homotopy and surgery theory, adapted to the realization problem for almost complex manifolds: namely, we give a characterization of the possible simply connected rational homotopy types, along with a choice of rational Chern classes and fundamental class, realized by simply connected closed almost complex manifolds in real dimensions six and greater. As a consequence, beyond demonstrating that rational homotopy types of closed almost complex manifolds are plenty, we observe that the realizability of a simply connected rational homotopy type by a simply connected closed almost complex manifold depends only on its cohomology ring. We conclude with some computations and examples.https://doi.org/10.1515/coma-2021-0133almost complex manifoldsrational homotopy theorychern classes32q6055p6257n6557r65 |
| spellingShingle | Milivojević Aleksandar On the characterization of rational homotopy types and Chern classes of closed almost complex manifolds Complex Manifolds almost complex manifolds rational homotopy theory chern classes 32q60 55p62 57n65 57r65 |
| title | On the characterization of rational homotopy types and Chern classes of closed almost complex manifolds |
| title_full | On the characterization of rational homotopy types and Chern classes of closed almost complex manifolds |
| title_fullStr | On the characterization of rational homotopy types and Chern classes of closed almost complex manifolds |
| title_full_unstemmed | On the characterization of rational homotopy types and Chern classes of closed almost complex manifolds |
| title_short | On the characterization of rational homotopy types and Chern classes of closed almost complex manifolds |
| title_sort | on the characterization of rational homotopy types and chern classes of closed almost complex manifolds |
| topic | almost complex manifolds rational homotopy theory chern classes 32q60 55p62 57n65 57r65 |
| url | https://doi.org/10.1515/coma-2021-0133 |
| work_keys_str_mv | AT milivojevicaleksandar onthecharacterizationofrationalhomotopytypesandchernclassesofclosedalmostcomplexmanifolds |