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

ISBN-10: 9400923996

ISBN-13: 9789400923997

ISBN-10: 9401075808

ISBN-13: 9789401075800

A NATO complicated research 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 used to be together supported through NATO and the common Sciences and Engineering examine Council of Canada, and used to be subsidized partly by way of the Canadian Mathematical Society. This e-book is the quantity of lawsuits for that assembly. Algebraic K-theory is basically the research of homotopy invariants bobbing up from jewelry and their linked matrix teams. extra importantly probably, the topic has develop into relevant to the research of the connection among Topology, Algebraic Geometry and quantity concept. It attracts on all of those fields as an issue in its personal correct, however it serves in addition to a good translator for the applying of ideas from one box in one other. The papers during this quantity are consultant of the present country of the topic. they're, for the main half, learn papers that are basically of curiosity to researchers within the box and to these desiring to be such. there's a part on difficulties during this quantity which may be of specific curiosity to scholars; it features a dialogue of the issues from Gersten's famous record of 1973, in addition to a quick record of latest problems.

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Representing integral cohomology classes. and Theorem: If M is a 00 C manifold. then with the notation above. there are exact sequences: (i) k ~. 2. 3 induces f. Then _k+1 02{f) €~. Z). oT = 01(f) f: ~(M) ~ such that - 02(f) with ffiIZ. m) The similarity between these sequences and those of Theorem is striking. and the analogy becomes transparent if we give a H. GIlLET AND C. E 41 somewhat different formulation of the differential character groups, following the article [9] of Cheeger. Suppose that M is a compact manifold; then by Poincare duality, we can compute the integral cohomology of M using chains rather than cochains: where we view C*(M) and n = dimension as a cochain complex with M.

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. Applications given are computing the holonomy of the Quillen connection and studying the Abel-Jacobi homomorphism. O. INTRODUCTION In this paper we sketch the relationship between the Arithmetic intersection theory introduced in [13] and the theory of differential characters developed by Cheeger and Simons in [10].

GIllET AND C. v2 }. v) l = Z. (E2 ,v2 ) and Also are bundles with connections. and then ~i(El·vl) U ~j(E2·v2)· i+j=p iii) If f: M ~ N is a map of manifolds. and with connection on N. v) is a bundle * (f E,f*v). Since Chern classes are integral and hence real. and the exterior derivative is a real operator. we can take the real part of the characteristic classes described above. ffiIZ) for p We obtain classes in A cp(E,v)rn ~ 0 which are characterized by axioms similar to those above except that i) is replaced by: i)rn If E is a line bundle and to the zero section of E.

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

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