Microlocal indices and Chern Classes of Foliations
Xia Liao, Xiping Zhang
TL;DR
This paper explores the microlocal approach to understanding global index formulas in one-dimensional holomorphic foliations, providing simplified proofs and extending existing formulas for various indices.
Contribution
It introduces new microlocal methods to derive and generalize index formulas for holomorphic foliations, enhancing theoretical understanding.
Findings
Unified microlocal framework for index formulas
Simplified proofs of Schwartz, GSV, and logarithmic indices
Generalizations of existing index formulas
Abstract
In this paper, we study how global index formulas arise in the theory of one-dimensional holomorphic foliation from the microlocal point of view. We give short proofs and generalizations to a few exisiting index formulas concerning Schwartz, GSV and logarithmic indices.
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Taxonomy
TopicsGeometry and complex manifolds · Quantum chaos and dynamical systems · Holomorphic and Operator Theory