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Paul Feehan: Morse-Bott theory on analytic spaces and applications to topology of smooth 4-manifolds

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Lukas Lewark

Paul Feehan: Morse-Bott theory on analytic spaces and applications to topology of smooth 4-manifolds

Abstract:

We describe a new approach to Morse theory on singular analytic spaces of the kind that typically arise in gauge theory, such as the moduli space of SO(3) monopoles over 4-manifolds or the moduli space of Higgs pairs over Riemann surfaces. We explain how this new version of Morse theory, called virtual Morse-Bott theory, can potentially be used to answer questions arising in the geography of 4-manifolds, such as whether constraints on the topology of compact complex surfaces of general type continue to hold for symplectic 4-manifolds or even for smooth 4-manifolds of Seiberg-Witten simple type. This is joint work with Tom Leness.

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