A Note on Donaldson's "Tamed to Compatible" Question

A Note on Donaldson's "Tamed to Compatible" Question

Year:    2014

Author:    Qiang Tan, Haifeng Xu

Communications in Mathematical Research , Vol. 30 (2014), Iss. 2 : pp. 179–182

Abstract

Recently, Tedi Draghici and Weiyi Zhang studied Donaldson's "tamed to compatible" question (Draghici T, Zhang W. A note on exact forms on almost complex manifolds. arXiv: 1111. 7287v1 [math. SG]. Submitted on 30 Nov. 2011). That is, for a compact almost complex 4-manifold whose almost complex structure is tamed by a symplectic form, is there a symplectic form compatible with this almost complex structure? They got several equivalent forms of this problem by studying the space of exact forms on such a manifold. With these equivalent forms, they proved a result which can be thought as a further partial answer to Donaldson's question in dimension 4. In this note, we give another simpler proof of their result.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.13447/j.1674-5647.2014.02.08

Communications in Mathematical Research , Vol. 30 (2014), Iss. 2 : pp. 179–182

Published online:    2014-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    4

Keywords:    compact almost complex 4-manifold $ω$-tame almost complex structure $ω$-compatible almost complex structure.

Author Details

Qiang Tan

Haifeng Xu