Localization and residue of the Bott class |
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Authors: | Taro Asuke |
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Institution: | Department of Mathematics, Faculty of Science, Hiroshima University, Japan |
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Abstract: | The Bott class of transversely holomorphic foliations is studied. We first introduce a formula which relates the Bott class and the Godbillon-Vey class. Then a ‘localizable part’ of the Bott class is defined. It is indeed localizable and written in terms of the Godbillon measure studied by Heitsch and Hurder. The above-mentioned formula is reviewed in terms of localizable parts. Finally, complex codimension-one foliations are considered. A version of residue is introduced and it is shown that the Bott class is ‘localized’ near the Julia set in the sense of Ghys-Gomez-Mont-Saludes. Some examples of calculation of the residue are presented. |
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Keywords: | Primary 57R30 Secondary 32S65 57R32 |
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