Abstract
In this chapter we prove two important results of Baum–Bott [3] and Camacho–Sad [10, 11], the first one concerning the computation of \(N_{\mathcal{F}}\cdot N_{\mathcal{F}}\) for a foliation \(\mathcal{F}\) on a compact surface, the second one concerning the computation of \(C \cdot C\) for a compact curve C invariant by a foliation. These two results, which are in fact two manifestations of the same “vanishing principle”, have a quite different nature than the easier formulae of the previous chapter: here the integrability of \(\mathcal{F}\) , that is the existence of leaves, plays a fundamental role. We shall also give several applications of these formulae. A comprehensive reference for these index theorems, and much beyond, is [45], especially Chapter V; see also [6, 7].
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Brunella, M. (2015). Index Theorems. In: Birational Geometry of Foliations. IMPA Monographs, vol 1. Springer, Cham. https://doi.org/10.1007/978-3-319-14310-1_3
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DOI: https://doi.org/10.1007/978-3-319-14310-1_3
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