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BY 4.0 license Open Access Published by De Gruyter Open Access May 6, 2022

On the characterization of rational homotopy types and Chern classes of closed almost complex manifolds

  • Aleksandar Milivojević EMAIL logo
From the journal 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 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.

MSC 2010: 32Q60; 55P62; 57N65; 57R65


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Received: 2021-09-19
Accepted: 2022-04-21
Published Online: 2022-05-06

© 2022 Aleksandar Milivojević, published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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