Complex sentence: At this time he was also assimilating de Rham's theorem, and defining the Hodge star operation which would allow him to define harmonic form and so refine the de Rham theory.
Split into simpler sentences: At this time he was also assimilating de Rham's theorem, and defining the Hodge star operation. It would allow him to define harmonic forms and so refine the de Rham theory.