My lecture this year studied the " differential geometry " aspect of generalized spaces such as the leaf space of a foliate. The " measure theory " and " topology " aspects had been explored during the 84-85 lecture. The plan is as follows :
I. Cycle over an algebra
II. Cyclic cohomology
III. Cyclic cohomology of a leaf algebra
IV. Cohomological translation of the longitudinal index theorem and secondary classes