Hodge cohomology of complete hyperKähler manifolds
Introductory Workshop: Special Geometric Structures and Analysis September 03, 2024 - September 06, 2024
Location: SLMath: Eisenbud Auditorium, Online/Virtual
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No Primary AMS MSC
Secondary Mathematics Subject Classification
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Hodge cohomology of complete hyperKähler manifolds
After reviewing the notion of L^2-cohomology and presenting various conjectures and recent results about the Hodge cohomology (in other words reduced L^2-cohomology) of some complete hyperKähler metrics, I will focus on a result of Hausel-Hunsicker-Mazzeo of 2004 describing the Hodge cohomology of most types of gravitational instantons. In particular, I will explain how this result crucially relies on a decay at infinity of L^2-harmonic forms which will be the object of the next lecture.
Hodge cohomology of complete hyperKähler manifolds
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