Determinant Line Bundles Revisited
Daniel S. Freed
TL;DR
This paper revisits the theory of determinant line bundles, providing simplified proofs for curvature and holonomy formulas related to Dirac operators on manifolds with boundary, based on eta invariants.
Contribution
It offers a simpler proof of curvature and holonomy formulas for determinant line bundles associated with Dirac operators, building on eta invariants on manifolds with boundary.
Findings
Simplified proofs of curvature formulas
Simplified proofs of holonomy formulas
Application of eta invariants to boundary problems
Abstract
This is a note for the conference proceedings Topological and Geometrical Problems related to Quantum Field Theory. We summarize our joint work with Dai about eta invariants on manifolds with boundary. Then we apply these results to prove the curvature and holonomy formulas for the natural connection on the determinant line bundle of a family of Dirac operators. These were originally proved by Bismut and the author--the proofs here are much simpler.
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Taxonomy
TopicsAdvanced Operator Algebra Research · Homotopy and Cohomology in Algebraic Topology · Geometric and Algebraic Topology