Global Analysis on Foliated Spaces (Mathematical Sciences Research Institute Publications)
Editorial Reviews
Review
Praise for the first edition ... 'The quest for the proof leads through functional analysis, C^* and von Neumann algebras, topological groupoids, characteristic classes and K-theory along a foliation, and the theory of pseudodifferential operators. It is a long but very rewarding journey and Moore and Schochet have performed a valuable service in putting all this material in one place in an easily readable form ... The book contains a wealth of information. It is not for those who wish an overview...However, for those wishing a comprehensive proof ... this book is indispensable.' AMS Bulletin
Book Description
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. 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 book presents a complete proof of this beautiful result, generalized to foliated spaces (not just manifolds).
Global Analysis on Foliated Spaces (Mathematical Sciences Research Institute Publications)
Global Analysis on Foliated Spaces (Mathematical Sciences Research Institute Publications),Calvin C. Moore,Claude L. Schochet,Silvio Levy,Cambridge University Press,0521613051,Foliations (Mathematics),Global analysis (Mathematics),Mathematics,Medical,Reference,Surgery - General,Topology - General,Analytic geometry,Mathematics / Applied
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