Harmonic Vector Fields

Appendix A. Twisted Cohomologies

Appendix A is devoted to briefly reviewing a few notions and results on the twisted cohomology of a pseudocomplex of cochains following S. Halperin & D. Lehmann (1975) with an application to the Dolbeau pseudocomplex of the almost complex manifold .

Keywords: Twisted cohomology; Dolbeau pseudocomplex; Cauchy-Riemann equations; holomorphic function; Dolbeau cohomology groups.

As previously seen (cf. Proposition 1.13 and Theorem 1.17 in Chapter 1) the isotropic almost complex structures J_δ,σ on T( M) are rarely integrable. It is therefore natural to look at the twisted Dolbeau cohomology of the almost complex manifold ...