A Mini-Course on Recent Progress in Algebraic K-Theory and its Relationship with Topology and Analysis
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چکیده
We attempt to survey some of the interrelationships between algebraic K-theory, topology, and analysis. The exposition is in two parts, the first dealing with K-theory of group rings and connections with topology, and the second dealing with flat bundles, secondary invariants, and connections with differential geometry.
منابع مشابه
RECENT PROGRESS IN ALGEBRAIC K–THEORY AND ITS RELATIONSHIP WITH TOPOLOGY AND ANALYSIS Mini-Course Notes by Jonathan Rosenberg Brief Outline I. “Assembly, Novikov Conjectures, and Control”. A. Classical applications of the K-theory of group rings B. Assembly and standard examples
k — a regular commutative ring. (Main case of interest, as we shall see, is k = Z.) kG — the group ring over k of a group G. BG — the classifying space of G, a space with contractible universal cover and fundamental group G. Unique up to homotopy equivalence. Has the property that H∗(BG) is the Eilenberg-MacLane homology of G. K(R) — the (non-connective) K-theory spectrum of a ring R. If one ig...
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تاریخ انتشار 2012