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.
The index of Dirac operators on manifolds with fibered boundaries / Eric, Leichtnam; Rafe, Mazzeo; Piazza, Paolo. - In: BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY SIMON STEVIN. - ISSN 1370-1444. - STAMPA. - 13:5(2006), pp. 845-855.
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Titolo: | The index of Dirac operators on manifolds with fibered boundaries | |
Autori: | ||
Data di pubblicazione: | 2006 | |
Rivista: | ||
Citazione: | The index of Dirac operators on manifolds with fibered boundaries / Eric, Leichtnam; Rafe, Mazzeo; Piazza, Paolo. - In: BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY SIMON STEVIN. - ISSN 1370-1444. - STAMPA. - 13:5(2006), pp. 845-855. | |
Handle: | http://hdl.handle.net/11573/50357 | |
Appartiene alla tipologia: | 01a Articolo in rivista |