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

created by daniele on 22 May 2017
modified on 04 Jul 2017

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Submitted Paper

Inserted: 22 may 2017
Last Updated: 4 jul 2017

Journal: arXiv:1705.10518 [math.DG]
Year: 2017
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 \cite{gray} and \cite{ugarte}, 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 \cite{mchugh-1}, where the Bott-Chern cohomology of hypothetical complex structures on $S^6$ is studied. The material is not intended to be original.