Asian Journal of Mathematics
- Asian J. Math.
- Volume 17, Number 2 (2013), 265-320.
The Atiyah-Patodi-Singer index theorem for Dirac operators over C*-algebras
We prove a higher Atiyah–Patodi–Singer index theorem for Dirac operators twisted by $C^*$-vector bundles. We use it to derive a general product formula for $\eta$-forms and to define and study new $\rho$-invariants generalizing Lott’s higher $\rho$-form. The higher Atiyah–Patodi–Singer index theorem of Leichtnam–Piazza can be recovered by applying the theorem to Dirac operators twisted by the Mishenko–Fomenko bundle associated to the reduced $C^*$-algebra of the fundamental group.
Asian J. Math. Volume 17, Number 2 (2013), 265-320.
First available in Project Euclid: 8 November 2013
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Wahl, Charlotte. The Atiyah-Patodi-Singer index theorem for Dirac operators over C*-algebras. Asian J. Math. 17 (2013), no. 2, 265--320.https://projecteuclid.org/euclid.ajm/1383923852