Back to Search
Start Over
On Bott-Chern and Aeppli cohomologies of almost complex manifolds and related spaces of harmonic forms
- Publication Year :
- 2023
-
Abstract
- In this paper we introduce several new cohomologies of almost complex manifolds, among which stands a generalization of Bott-Chern and Aeppli cohomologies defined using the operators $d$, $d^c$. We explain how they are connected to already existing cohomologies of almost complex manifolds and we study the spaces of harmonic forms associated to $d$, $d^c$, showing their relation with Bott-Chern and Aeppli cohomologies and to other well-studied spaces of harmonic forms. Notably, Bott-Chern cohomology of $1$-forms is finite-dimensional on compact manifolds and provides an almost complex invariant $h^1_{d + d^c}$ that distinguishes between almost complex structures. On almost K\"ahler $4$-manifolds, the spaces of harmonic forms we consider are particularly well-behaved and are linked to harmonic forms considered by Tseng and Yau in the study of symplectic cohomology.<br />Comment: 34 pages
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2303.17449
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1016/j.exmath.2023.09.001