Foliated spaces look locally like products, but their global structure is generally not a product, and tangential differential operators are correspondingly more complex. In the 1980s, Alain Connes founded what is now known as noncommutative geometry and topology. One of the first results was his generalization of the Atiyah-Singer index theorem to compute the analytic index associated with a tangential (pseudo) - differential operator and an invariant transverse measure on a foliated manifold, in terms of topological data on the manifold and the operator. This second edition presents a complete proof of this beautiful result, generalized to foliated spaces (not just manifolds). It includes the necessary background from analysis, geometry, and topology. The present edition has improved exposition, an updated bibliography, an index, and additional material covering developments and applications since the first edition came out, including the confirmation of the Gap Labeling Conjecture of Jean Bellissard.
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在葉狀空間的平颱上，把微分幾何、特徵類、算子代數、僞微分算子、指標定理等等重新擼瞭一遍。
评分在葉狀空間的平颱上，把微分幾何、特徵類、算子代數、僞微分算子、指標定理等等重新擼瞭一遍。
评分在葉狀空間的平颱上，把微分幾何、特徵類、算子代數、僞微分算子、指標定理等等重新擼瞭一遍。
评分在葉狀空間的平颱上，把微分幾何、特徵類、算子代數、僞微分算子、指標定理等等重新擼瞭一遍。
评分在葉狀空間的平颱上，把微分幾何、特徵類、算子代數、僞微分算子、指標定理等等重新擼瞭一遍。
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