Narrowing Cohomology for Complex S^6

Andrew Patrick McHugh

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 $a = h_{\bar{\partial}}^{2,0}-h_{\bar{\partial}}^{1,0}$, $c = h_{\bar{\partial}}^{0,2}$,$d = h_{\bar{\partial}}^{1,2}$, $h_{\bar{\partial}}^{2,0}$, $h_{BC}^{1,1}$, 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 $h^{2,0} = a = c = d =0$.

Keywords

six sphere, complex structure, Hodge numbers, Aeppli cohomology, Bott-Chern cohomology

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