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An analytic proof of Novikov’s theorem on rational Pontrjagin classes. (English) Zbl 0531.58045
The authors give an analytic proof of topological invariance of rational Pontryagin classes of a compact smooth manifold. The proof is a consequence of the second author’s results on signature operators on Lipschitz manifolds (see the preceding review) combined with the first author’s theorem [Geometric topology, Proc. Conf., Athens/Ga. 1977, 543- 555 (1979; Zbl 0478.57007)] on existence of an essentially unique Lipschitz structure on any topological manifold of dimension 4.
Reviewer: J.Dodziuk

MSC:
58J20Index theory and related fixed point theorems (PDE on manifolds)
57R20Characteristic classes and numbers (differential topology)
57N65Algebraic topology of manifolds
58J22Exotic index theories (PDE on manifolds)
57Q99PL-topology
47A53(Semi-)Fredholm operators; index theories
References:
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[2]J. W. Milnor, J. D. Stasheff,Characteristic Classes, Princeton, 1974.
[3]S. P. Novikov, Topological Invariance of rational Pontrjagin Classes,Doklady A.N.S.S.S.R.,163 (2) (1965), 921–923.
[4]I. M. Singer, Future Extension of Index Theory and Elliptic Operators, in Prospects in Mathematics,Annals of Math. Studies,70 (1971), 171–185.
[5]D. Sullivan, Hyperbolic Geometry and Homeomorphisms, inGeometric Topology, Proc. Georgia Topology Conf. Athens, Georgia, 1977, 543–555, ed. J. C. Cantrell, Academic Press, 1979.
[6]N. Teleman, The index of Signature Operators on Lipschitz Manifolds,Publ. Math. I.H.E.S., this volume, 39–78.
[7]P. Tukia, J. Väisälä, Lipschitz and quasiconformal approximation and extension,Ann. Acad. Sci. Fenn. Ser. A,16 (1981), 303–342.
[8]———-, Quasiconformal extension from dimensionn ton + 1,Annals of Math.,115 (1982), 331–348. · Zbl 0484.30017 · doi:10.2307/1971394