Narrowing Cohomology for Complex S^6

Abstract

We compute Bott Chern, and Aeppli cohomology for a complex structure on the six sphere, $S^6$.

We also give a table for the hodge numbers for the Bott-Chern (and thus also Aeppli) cohomology where hodge numbers are given in terms of whole number parameters $a=h_{\overline{\partial }}^{2,0}-h_{\overline{\partial }}^{1,0}$, $c=h_{\overline{\partial }}^{0,2}$,$d=h_{\overline{\partial }}^{1,2}$, $h_{\overline{\partial }}^{2,0}$, $h_{BC}^{1,1}$, and $h_{BC}^{2,2}$.

As an example, we work out the Bott-Chern hodge numbers completely in the hypothetical case that the Dolbeault cohomology has $h^{2,0}=a=c=d=0$.