The families Clifford index and differential KO-theory

2023/03/16 by Daniel Berwick-Evans, Berwick-Evans, Daniel
Mathematics · #Advanced Topics in Algebra #Advanced Operator Algebra Research #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.2303.09091

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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