References
[A1]Atiyah, M. F., Global theory of elliptic operators.Proc. Int. Conf. Functional Analysis and Related Topics, Tokyo (1969), 21–30.
[A2]Atiyah, M. F. A survey ofK-theory, inK-theory and operator algebras, Athens, Georgia 1975. Springer Lecture Notes no. 575, 1–9.
[A.S.]Atiyah, M. F. &Singer, I. M., The index of elliptic operators, Part III.Ann. of Math., 87 (1968), 546–604.
[B.D.F.]Brown, L. G., Douglas, R. G. &Fillmore, P. A., Extensions ofC *-algebras andK-homology.Ann. of Math., 105 (1977), 265–324.
[B.F.M.]Baum, P., Fulton, W. &MacPherson, R., Riemann-Roch for singular varieties.Publ. Math. I.H.E.S., 45 (1975), 101–167.
[B.J.]Baaj, S. &Julg, P., Théorie bivariante de Kasparov et opérateurs non bornés dans lesC *-modules hilbertiens.C. R. Acad. Sci. Paris, 296 (1983), 875–878.
[C]Cheeger, J., On the Hodge theory on Riemannian pseudomanifolds.Proc. Symp. Pure Math., A.M.S., 36 (1980), 91–146.
[H1]Hilsum, M., Opérateurs de signature sur une varieté Lipschitzienne et modules de Kasparov non bornés.C. R. Acad. Sci. Paris, 297 (1983), 49–52.
[H2]Hilton, P.,General cohomology theory and K-theory. London Math. Soc. Lecture Note Series, 1 (1971).
[H3]Hirzebruch, F.,Topological methods in algebraic geometry. 3rd Edition, Springer-Verlag, 1966.
[K]Kasparov, G. G., Topological invariants of elliptic operators, I:K-homology.Math. USSR-Izv., 9 (1975), 751–792 (english translation).
[K.S.]Kirby, R. & Siebenmann, L.,Foundational essays on topological manifolds, smoothings and triangulations. Annals of Math. Studies, Vol. 88 (1977), Princeton.
[L.T.]Luukkainen, J. &Tukia, P., Quasisymmetric and Lipschitz approximation of embeddings.Ann. Acad. Sci. Fenn. Ser. A Math., 6 (1981), 343–368.
[N]Novikov, S. P., Topological invariance of rational Pontrjagin classes.Dokl. Akad. Nauk SSSR, 163 (1965), 921–923.
[P]Palais, R. S.,Seminar on the Atiyah-Singer index theorem. Annals of Math. Studies, Vol. 57 (1965), Princeton.
[R.S.]Rourke, C. P. &Sanderson, B. J., On topological neighborhoods.Compositio Math., 22 (1970), 387–424.
[Si]Singer, I. M.,Future extensions of index theory and elliptic operators. Annals of Math. Studies, Vol. 70 (1971), Princeton, 171–185.
[Su1]Sullivan, D.,Geometric topology, Part 1. M.I.T. Notes (1969).
[Su2]Sullivan, D., Hyperbolic geometry and homeomorphisms, inGeometric topology, Proc. Georgia Topology Conf., Athens, Georgia 1977, 543–555. Ed. J. C. Cantrell, Academic Press, 1979.
[S.T.]Sullivan, D. &Teleman, N., An analytical proof of Novikov’s theorem on rational Pontriagin classes.Publ. Math. I.H.E.S., 58 (1983), 79–82.
[T1]Teleman, N., Global analysis onPL-manifolds.Trans. Amer. Math. Soc., 256 (1979), 49–88.
[T2] —, Combinatorial Hodge theory and signature operator.Invent. Math., 61 (1980), 227–249.
[T3] —, The index of signature operators on Lipschitz manifolds.Publ. Math. I.H.E.S., 58 (1983), 39–78.
[T.V.]Tukia, P. &Väisälä, J., Lipschitz and quasiconformal approximation and extension.Ann. Acad. Sci. Fenn. Ser. A. Math., 6 (1981), 303–342.
Author information
Authors and Affiliations
Additional information
Dedicated to M. F. Atiyah and I. M. Singer
Partially supported by the N.S.F. Grant No. MCS 8102758.
Rights and permissions
About this article
Cite this article
Teleman, N. The index theorem for topological manifolds. Acta Math. 153, 117–152 (1984). https://doi.org/10.1007/BF02392376
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02392376