Maximally non-integrable almost complex structures: an h-principle and cohomological properties

Coelho, R.; Placini, G. and Stelzig, J. (2022): Maximally non-integrable almost complex structures: an h-principle and cohomological properties. In: Selecta Mathematica, New Series (SM), Vol. 28, No. 5

Abstract

We study almost complex structures with lower bounds on the rank of the Nijenhuis tensor. Namely, we show that they satisfy an h-principle. As a consequence, all parallelizable manifolds and all manifolds of dimension 2n > 10 (respectively > 6) admit a almost complex structure whose Nijenhuis tensor has maximal rank everywhere (resp. is nowhere trivial). For closed 4-manifolds, the existence of such structures is characterized in terms of topological invariants. Moreover, we show that the Dolbeault cohomology of non-integrable almost complex structures is often infinite dimensional (even on compact manifolds).

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 1022-1824
• Language: English
• DFG: Gefördert durch die Deutsche Forschungsgemeinschaft (DFG) - 491502892