# Hodge numbers of a hypothetical complex structure on $S^6$

created by daniele on 22 May 2017
modified on 06 Feb 2018

[BibTeX]

Published Paper

Inserted: 22 may 2017
Last Updated: 6 feb 2018

Journal: Differ. Geom. Appl.
Volume: 57
Pages: 105-120
Year: 2018
Doi: 10.1016/j.difgeo.2017.10.012

ArXiv: 1705.10518 PDF
These are the notes for the talk "Hodge numbers of a hypothetical complex structure on $S^6$" given by the author at the MAM1 "(Non)-existence of complex structures on $S^6$" held in Marburg in March 2017. They are based on A. Gray, A property of a hypothetical complex structure on the six sphere, Boll. Un. Mat. Ital. B (7)} $\textbf{11}$ (1997), Suppl. fasc. 2, 251--255. and L. Ugarte, Hodge numbers of a hypothetical complex structure on the six sphere, Geom. Dedicata $\textbf{81}$ (2000), no. 1-3, 173--179., where Hodge numbers and the dimensions of the succesive pages of the Fr\"olicher spectral sequence for $S^6$ endowed with a hypothetical complex structure are investigated. We also add results from Andrew McHugh, Narrowing cohomologies on complex $S^6$, Eur. J. Pure Appl. Math. $\textbf{10}$ (2017), no. 3, 440--454., where the Bott-Chern cohomology of hypothetical complex structures on $S^6$ is studied. The material is not intended to be original.