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Google圖書搜尋
Index Theory of Elliptic Operators, Foliations, and Operator Algebras
Jerome Kaminker
Kenneth C. Millett
American Mathematical Society
其他書名
Proceedings of AMS Special Sessions Held January 7, 1986 and April 11, 1986
出版
American Mathematical Soc.
, 1988
主題
Mathematics / Functional Analysis
ISBN
0821850776
9780821850770
URL
http://books.google.com.hk/books?id=mOgbCAAAQBAJ&hl=&source=gbs_api
EBook
SAMPLE
註釋
Combining analysis, geometry, and topology, this volume provides an introduction to current ideas involving the application of $K$-theory of operator algebras to index theory and geometry. In particular, the articles follow two main themes: the use of operator algebras to reflect properties of geometric objects and the application of index theory in settings where the relevant elliptic operators are invertible modulo a $C^*$-algebra other than that of the compact operators. The papers in this collection are the proceedings of the special sessions held at two AMS meetings: the Annual meeting in New Orleans in January 1986, and the Central Section meeting in April 1986. Jonathan Rosenberg's exposition supplies the best available introduction to Kasparov's $KK$-theory and its applications to representation theory and geometry. A striking application of these ideas is found in Thierry Fack's paper, which provides a complete and detailed proof of the Novikov Conjecture for fundamental groups of manifolds of non-positive curvature. Some of the papers involve Connes' foliation algebra and its $K$-theory, while others examine $C^*$-algebras associated to groups and group actions on spaces.