The index of Dirac operators on manifolds with fibered boundaries

Eric, Leichtnam; Rafe, Mazzeo; Paolo, Piazza

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Let X be a compact manifold with boundary ∂X, and suppose that ∂X is the total space of a fibration Z → ∂X → Y. Let D Φ be a generalized Dirac operator associated to a Φ-metric gΦ on X. Under the assumption that DΦ is fully elliptic we prove an index formula for DΦ. The proof is in two steps: first, using results of Melrose and Rochon, we show that the index is unchanged if we pass to a certain b-metric gb(ε). Next we write the b- (i.e. the APS) index formula for gb(ε); the Φ-index formula follows by analyzing the limiting behaviour as ε ↘ 0 of the two terms in the formula. The interior term is studied directly whereas the adiabatic limit formula for the eta invariant follows from work of Bismut and Cheeger.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11573/50357

Titolo:	The index of Dirac operators on manifolds with fibered boundaries
Autori interni:	PIAZZA, Paolo
Data di pubblicazione:	2006
Rivista:	BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY SIMON STEVIN
Abstract:	Let X be a compact manifold with boundary ∂X, and suppose that ∂X is the total space of a fibration Z → ∂X → Y. Let D Φ be a generalized Dirac operator associated to a Φ-metric gΦ on X. Under the assumption that DΦ is fully elliptic we prove an index formula for DΦ. The proof is in two steps: first, using results of Melrose and Rochon, we show that the index is unchanged if we pass to a certain b-metric gb(ε). Next we write the b- (i.e. the APS) index formula for gb(ε); the Φ-index formula follows by analyzing the limiting behaviour as ε ↘ 0 of the two terms in the formula. The interior term is studied directly whereas the adiabatic limit formula for the eta invariant follows from work of Bismut and Cheeger.
Handle:	http://hdl.handle.net/11573/50357
Appare nelle tipologie:	01.a Pubblicazione su Rivista

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