caa a22 4500 386386102 CHVBK 20180307112058.0 cr unu---uuuuu 161130e198911 xx s 000 0 eng 10.1017/S0305004100068213 doi S0305004100068213 pii (NATIONALLICENCE)cambridge-10.1017/S0305004100068213 K-theory of real algebraic surfaces and threefolds [Elektronische Daten] Let X be an affine real algebraic variety, i.e., up to biregular isomorphism an algebraic subset of n. (For definitions and notions of real algebraic geometry we refer the reader to the book [6].) Let denote the ring of regular functions on X ([6], chapter 3). (If X is an algebraic subset of n then is comprised of all functions of the form f/g, where g, f: X → are polynomial functions with g−1(O) = Ø.) In this paper, assuming that X is compact, non-singular, and that dim X ≤ 3, we compute the Grothendieck group of projective modules over (cf. Section 1), and the Grothendieck group and the Witt group of symplectic spaces over (cf. Section 2), in terms of the algebraic cohomology groups and generated by the cohomology classes associated with the algebraic subvarieties of X. We also relate the group to the Grothendieck group KO(X) of continuous real vector bundles over X, and the groups and to the Grothendieck group K(X) of continuous complex vector bundles over X. Copyright © Cambridge Philosophical Society 1989 Bochnak J. Department of Mathematics, Vrije Universiteit, P.O. Box 7161, 1007 MC Amsterdam, The Netherlands Kucharz W. Department of Mathematics and Statistics, University of New Mexico, Albuquerque, NM 87131, U.S.A. Mathematical Proceedings of the Cambridge Philosophical Society Cambridge University Press 106/3(1989-11), 471-480 0305-0041 106:3<471 1989 106 PSP https://doi.org/10.1017/S0305004100068213 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0305004100068213 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Bochnak J. Department of Mathematics, Vrije Universiteit, P.O. Box 7161, 1007 MC Amsterdam, The Netherlands NATIONALLICENCE 700 1- Kucharz W. Department of Mathematics and Statistics, University of New Mexico, Albuquerque, NM 87131, U.S.A NATIONALLICENCE 773 0- Mathematical Proceedings of the Cambridge Philosophical Society Cambridge University Press 106/3(1989-11), 471-480 0305-0041 106:3<471 1989 106 PSP CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge