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

Abstract

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)} $\text{11}$ (1997), Suppl. fasc. 2, 251--255.] and [L. Ugarte, Hodge numbers of a hypothetical complex structure on the six sphere, Geom. Dedicata $\text{81}$ (2000), no. 1-3, 173--179.], where Hodge numbers and the dimensions of the succesive pages of the Frölicher 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. $\text{10}$ (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.

Notes for the MAM1 "(Non)-existence of complex structures on $S^6$" held in Marburg in March 2017

Cited by in corpus (4)

• On the Structure of Double Complexes
• On the history of the Hopf problem
• The complex geometry of a hypothetical complex structure on $S^6$
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