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arXiv · 1009.4272

Pseudodifferential operators on manifolds with foliated boundaries

Frédéric Rochon
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Abstract

Let X be a smooth compact manifold with boundary. For smooth foliations on the boundary of X admitting a `resolution' in terms of a fibration, we construct a pseudodifferential calculus generalizing the fibred cusp calculus of Mazzeo and Melrose. In particular, we introduce certain symbols leading to a simple description of the Fredholm operators inside the calculus. When the leaves of the fibration `resolving' the foliation are compact, we also obtain an index formula for Fredholm perturbations of Dirac-type operators. Along the way, we obtain a formula for the adiabatic limit of the eta invariant for invertible perturbations of Dirac-type operators, a result of independent interest generalizing the well-known formula of Bismut and Cheeger.

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Frédéric Rochon. 2011-12-20. Pseudodifferential operators on manifolds with foliated boundaries. https://arxiv.org/abs/1009.4272

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