Some Applications of Topological K-Theory
Some applications of topological K-theory
Atiyah and Hirzebruch considered a topological analog defined for any compact space X, a group K{X) constructed from the category of vector bundles on X. It is this ''topological K-theory" that this book will study.
This book describes a bivariant K-theory for bornological algebras, which provides a vast generalization of topological K-theory. In addition, it details other approaches to bivariant K-theories for operator algebras.
In this last lecture I will present some applications of the homotopy theory of dg- categories. We will see in particular how the problems mentioned in Sect.1.2 can be solved using dg-categories. The very last section will be some ...
This book covers the connection between algebraic K-theory and Bökstedt, Hsiang and Madsen's topological cyclic homology and proves that the difference between the theories are ‘locally constant’.
We will not treat applications in detail; however, we will outline the most striking of the applications to date in a section at the end, as well as mentioning others at suitable points in the text.
The answer (known as Bloch's formula, see [Quillen, Theorem 5.19 and Srinivas, Corollary 5.27) is that CH*(X) = H*(X, Kk, x), where K*,x is the sheaf given by “sheafifying” the presheaf U → Kk(U), for U a Zariski-open subset of X.
[9] LAZAROV C. Secondary characteristic classes in K -theory, Trans. Amer. Math. Soc., 136 (1968), 36-59. [10] MAHAMMED N., PICCININI R. , SUTER U. Some applications of topological K -theory, North H olland Math. Studies 45, 1980.
[238] G.B. Segal: Operations in stable homotopy theory; New Developments in Topology, Cambridge Univ. ... [248] V.P. Snaith: Review of Some applications of topological K-theory by N. Ma- hammed, R. Piccinini and U. Suter; Bull.
This book demonstrates in the case of topology how these obstacles can be overcome, with enlightening results.... Within its chosen boundaries the coverage of this book is superb.