The families Clifford index and differential KO-theory
arXiv:2303.09091
Abstract
Extending ideas of Atiyah--Bott--Shapiro and Quillen, we construct a model for differential -theory whose cocycles are families of Clifford modules with superconnection. The model is built to accommodate an analytic pushforward for bundles of spin manifolds, affording a differential refinement of Atiyah and Singer's families index.
37 pages