Morse theory on moduli spaces of instantons on ALE scalar-flat Kähler surfaces
نویسنده
چکیده
LeBrun constructed a scalar-flat Kähler metric on the total space of Chern class −n line bundle O(−n) → CP1. We study moduli spaces of ASD connections on it. It is known that the natural L2-metrics on them are kählerian. We study them when the metric is complete. We give an algorithm to compute their Betti numbers. On the way of the proof, we also show that their homology groups have no torsion and vanish in odd degrees. Our method is the Morse theory, can be applied to a wider class of noncompact 4-manifolds.
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