Download Algebraic K-Theory: Connections with Geometry and Topology by Barry Dayton, Charles Weibel (auth.), J. F. Jardine, V. P. PDF

By Barry Dayton, Charles Weibel (auth.), J. F. Jardine, V. P. Snaith (eds.)

A NATO complex examine Institute entitled "Algebraic K-theory: Connections with Geometry and Topology" was once held on the Chateau Lake Louise, Lake Louise, Alberta, Canada from December 7 to December eleven of 1987. This assembly was once together supported through NATO and the typical Sciences and Engineering learn Council of Canada, and used to be subsidized partially through the Canadian Mathematical Society. This booklet is the amount of court cases for that assembly. Algebraic K-theory is largely the examine of homotopy invariants bobbing up from jewelry and their linked matrix teams. extra importantly might be, the topic has develop into primary to the research of the connection among Topology, Algebraic Geometry and quantity concept. It attracts on all of those fields as a subject matter in its personal correct, however it serves in addition to a good translator for the appliance of techniques from one box in one other. The papers during this quantity are consultant of the present nation of the topic. they're, for the main half, examine papers that are basically of curiosity to researchers within the box and to these meaning to be such. there's a part on difficulties during this quantity which could be of specific curiosity to scholars; it features a dialogue of the issues from Gersten's recognized record of 1973, in addition to a brief checklist of latest problems.

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H M. N. = d{f*~). ~ M - dim N. ~) a current such that Hence But = dim f*c f*(c - d~) c - as follows. f*~) 00 C N and represents a class in It is straightforward to show that the map f* is independent of the choices made. 3. If 00 E is a C complex vector bundle over M. suppose paracompact. 5. Z) Integral Chern classes p E. finding sections of E has two kinds of classes. which are the obstructions to M. C). ffi). In [10]. C). v) E. ffi) or deRham classes in obstructions to finding a flat connection on on which we E is a line bundle and the zero section of M - {mls{m) = O} E.

Ffi». rn)/~;(X». 4. The range of the map intermediate Jacobian of tp is isomorphic to the p-th (Griffiths) X: which is itself the range of the Griffiths' Abel-Jacobi homomorphism a description of which may be found in [IS]. In the next paragraph we eP . First we shall give an alternative shall identify ~p description of eP . C) be the complex of complex valued currents on X. with viewed as forms with distribution coefficients. C) the Hodge filtration on The induces an isomorphism on cohomology.

Module structures in the K-theory of graded rings', J. Algebra 105, 465-483, 1987. : 'Mayer-Vietoris sequences and module structures on NK*', Lecture Notes in Math. 854, Springer-Verlag, 1981. : 'Fibre spaces in algebraic geometry', [1949c], Oevres Scientifiques, Vol. I, Springer-Verlag, 1979. S. 35 route de Chartres 91440 Bures-sur-Yvette France ABSTRACT. This paper sketches the relationship between the arithmetic Chow groups introduced by the authors, and the theory of differential characters due to Cheeger and Simons.

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