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BIRS Workshop Lecture Videos

Quasi-fibered boundary pseudodifferential operators Rochon, Frédéric


Quasi-fibered boundary (QFB) metrics form a natural class of complete metrics generalizing the quasi-asymptotically locally Euclidean (QALE) metrics of Joyce. After recalling what those metrics are, I will explain how to construct a suitable pseudodifferential calculus containing good parametrices for operators like the Hodge-deRham operator of a QFB metric, allowing us to show that they are Fredholm when acting on suitable Sobolev spaces and yielding results about the decay of L2 harmonic forms. This in turn can be used to study the reduced L2 cohomology of some QFB metrics. This is a joint work with Chris Kottke.

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