The families Clifford index and differential KO-theory

Published 16 Mar 2023 in math.AT and math.DG | (2303.09091v1)

Abstract: Extending ideas of Atiyah--Bott--Shapiro and Quillen, we construct a model for differential $\rm KO$-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.

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Daniel Berwick-Evans

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