He examined a space acted on by an arbitrary Lie group of transformations developing a theory of moving frames which generalises the kinematical theory of Darboux In fact this work led Cartan to the notion of a fibre bundle although he does not give an explicit definition of the concept in his work

Could you correct the punctuation please?
He examined a space acted on by an arbitrary Lie group of transformations, developing a theory of moving frames which generalises the kinematical theory of Darboux . In fact this work led Cartan to the notion of a fibre bundle although he does not give an explicit definition of the concept in his work.