Generalized complex structures on 4-manifolds

Thumbnail Image

Persistent link to this item

View Statistics

Journal Title

Journal ISSN

Volume Title


Generalized complex structures on 4-manifolds

Published Date




Thesis or Dissertation


We study the existence of generalized complex structures on closed smooth fourmanifolds in this thesis. We first prove an integrability theorem of generalized complex structures in terms of almost bihermitian structures. After reviewing the results of type zero and type two generalized complex structures, we prove the necessary and sufficient topological conditions for the existence of type one generalized complex structures on compact four-manifolds. We also obtain a nonexistence result of T2-invariant untwisted generalized complex structures with mixed types on the four torus T4. Finally, we prove a result about finite group actions on tamed almost complex four-manifolds.


University of Minnesota Ph.D. dissertation. May 2013. Major: Mathematics. Advisor: Tian-Jun Li. 1 computer file (PDF); iv, 71 pages.

Related to




Series/Report Number

Funding information

Isbn identifier

Doi identifier

Previously Published Citation

Suggested citation

Chen, Haojie. (2013). Generalized complex structures on 4-manifolds. Retrieved from the University Digital Conservancy,

Content distributed via the University Digital Conservancy may be subject to additional license and use restrictions applied by the depositor. By using these files, users agree to the Terms of Use. Materials in the UDC may contain content that is disturbing and/or harmful. For more information, please see our statement on harmful content in digital repositories.