"Invertomerism" is frankly a new word to me, but taking a stab at a long-unanswered question: trialkylamine compounds are sort-of-but-not-really chiral. "Sort of" because the nitrogen is not planar; "not really" because it's not all that hard to invert. The energy barrier for the inversion of ammonia is only about 24 kJ/mol, and ammonia "turns itself inside out" pretty rapidly even at room temperature.
Invertomerism of trialkylamines refers to the phenomenon where the three alkyl groups attached to the nitrogen atom (tertiary amine) can rearrange their positions by undergoing inversion at the nitrogen center. This inversion results in two distinct forms of the trialkylamine molecule that interconvert rapidly at room temperature.