References
Atiyah, M.F.: Elliptic operators and compact groups. (Lecture Notes in Math., vol. 401). Berlin Heidelberg New York: Springer 1974
Atiyah, M.F.: Elliptic operators, discrete groups and von Neumann algebras. Astèrisque32/33, 43–72 (1976)
Atiyah, M.F., Patodi, V., Singer, I.M.: Spectral asymmetry and Riemannian geometry. Bull. Lond. Math. Soc.5, 229–234 (1973)
Atiyah, M.F., Patodi, V., Singer, I.M.: Spectral asymmetry and Riemannian geometry, I. Math. Proc. Camb. Philos. Soc.77, 43–69 (1975)
Atiyah, M.F., Patodi, V., Singer, I.M.: Spectral asymmetry and Riemannian geometry, II. Math. Proc. Camb. Philos. Soc.78, 43–69 (1975)
Atiyah, M.F., Patodi, V., Singer, I.M.: Spectral asymmetry and Riemannian geometry, III. Math. Proc. Camb. Philos. Soc.79, 71–99 (1975)
Atiyah, M.F., Singer, I.M.: The index of elliptic operators, I. Ann. Math.87, 484–530 (1968)
Atiyah, M.F., Singer, I.M.: Index theory for skew-adjoint Fredholm operators. Publ. Math., Inst. Hautes Etud. Sci.37, 305–326 (1969)
Baum, P., Connes, A.:K-Theory for actions of discrete groups. I.H.E.S Preprint 1985
Baum, P., Connes, A.: Chern character for discrete groups. In: A Fête of topology, pp. 163–232. New York: North-Holland 1987
Baum, P., Douglas, R.G.:K-homology and index theory. In: Operator algebras and applications. Proc. Symp. Pure Math.38, 117–173 (1982)
Baum, P., Douglas, R.G.: Toeplitz operators and Poincaré duality. In: Proc. Toeplitz memorial Conf., Tel Aviv 1981, pp. 137–166. Basel: Birkhäuser 1982
Bismut, J.-M., Freed, D.: The analysis of elliptic families: II. Dirac operators, eta invariants and the holonomy theorem. Commun. Math. Phys.107, 103–163 (1986)
Brown, L.G., Douglas, R.G., Filmore, P.A.: Extensions ofC *-algebras andK-homology. Ann. Math.105, 265–324 (1977)
Camacho, C., Neto, A.L.: Geometric theory of foliations. Basel: Birkhäuser 1985
Cartan, H.: Cohomologie réelle d'un espace fibré principal différentiable. Seminaire H. Cartan, E.N.S. 1949/50, 20–01 á 20–11
Cheeger, J., Gromov, M.: On the characteristic numbers of complete manifolds of bounded curvature and finite volume. In: Differential geometry and complex analysis, pp. 115–154. Chavel, I., Farkas, H. (eds.). Berlin Heidelberg New York: Springer 1985
Cheeger, J., Gromov, M.: Bounds on the von Neumann dimension ofL 2-cohomology and the Gauss-Bonnet theorem for open manifolds. J. Differ. Geom.21, 1–34 (1985)
Cheeger, J., Gromov, M., Taylor, M.: Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds. J. Differ. Geom.17, 15–54 (1982)
Cheeger, J., Simons, J.: Differential characters and geometric invariants. Preprint (1972); Appeared in: Geometry and topology. Proceedings, Univ. of Maryland 1983–84, (Lecture Notes in Math., vol. 1167, pp. 50–80). Berlin Heidelberg New York: Springer 1986
Chen, S.Y., Li, P., Yau, S.-T.: On the upper estimate of the heat kernel of a complete Riemannian manifold. Am. J. Math.103, 1021–1063 (1981)
Chernoff, P.R.: Essential self-adjointness of powers of generators of hyperbolic equations. J. Funct. Anal.12, 401–414 (1973)
Coburn, L.A., Douglas, R.G.:C *-algebras of operators on a half space, I. Publ. Math., Inst. Hautes Etud. Sci.40, 59–67 (1971)
Coburn, L.A., Douglas, R.G., Schaeffer, D.S., Singer, I.M.:C *-algebras of operators on a half-space, II: Index theory. Publ. Math. Inst. Hautes Etud. Sci.40, 69–79 (1971)
Coburn, L.A., Moyer, R., Singer, I.M.:C *-algebras of almost periodic pseudo-differential operators. Acta Math.130, 279–307 (1973)
Connes, A.: The von Neumann algebra of a foliation. (Lecture Notes in Physics, vol. 80, pp. 145–151). Berlin Heidelberg New York: Springer 1978
Connes, A.: Sur la théorie non-commutative de l'integration. (Lecture Notes in Math., vol. 725, pp. 19–143). Berlin Heidelberg New York: Springer 1979
Connes, A.: A survey of foliations and operator algebras. In: Operator algebras and applications. Proc. Symp. Pure Math.38, 521–628 (1982)
Connes, A.: Non-commutative differential geometry. I. The Chern Character. I.H.E.S. Preprint. (1982) no. IHES/M/82/53
Connes, A.: Non-commutative differential geometry. I. The Chern character inK-homology. Publ. Math., Inst. Hautes Etud. Sci.62, 41–93 (1986)
Connes, A.: Non-commutative differential geometry. II. deRham homology and non-commutative algebra. Publ. Math., Inst. Hautes Etud. Sci.62, 94–144 (1986)
Connes, A.: Cyclic cohomology and the transverse fundamental class of foliation. In: Geometric methods in operator algebras, Araki, H., Effros, E.G., (eds.). Pitman Res. Notes, Math. Ser.123, 52–144 (1986)
Connes, A.: Entire cyclic cohomology of Banach algebras and characters of 0-summable Fredholm modules.K-Theory1, 519–548 (1988)
Connes, A., Skandalis, G.: The longitudinal index theorem for foliations. Publ. Res. Inst.20, 1139–1183 (1984)
Curto, R., Muhly, P., Xia, J.: Toeplitz operators on flows. J. Funct. Anal. (to appear)
Donnelly, H.: Eta invariants forG-spaces. Indiana Univ. Math. J.27, 889–918 (1978)
Donnelly, H.: Eta invariant of a fibered manifold. Topology15, 247–252 (1976)
Douglas, R.G.:C *-algebra extensions andK-homology. Ann. Math. Stud.95, 1–8 (1980)
Douglas, R.G.: Elliptic invariants for differential operators. In: Proc. Symp. on the Mathematical Heritage of Hermann Weyl. Proc. Symp. Pure Math.48, 275–284 (1988)
Douglas, R.G.: Elliptic invariants and operator algebras: toroidal examples. In: Operator algebras and applications, vol. I: Structure theory;K-theory, geometry and topology. (London Math. Soc. Lect. Notes, vol. 136, pp. 61–79). Cambridge: Cambridge Univ. Press 1988
Douglas, R.G.: Another look at real-valued index theory. In: Surveys of some recent results in operator theory, vol. II, Conway, J.B., Morrel, B.B. (eds.). Pitman Res. Notes Math. Ser.192, 91–120 (1988)
Douglas, R.G., Hurder, S., Kaminker, J.: The eta invariant, foliation algebras, and cyclic cocycles. Math. Sci. Res. Inst., Berkeley, Preprint no. 14711-85 (1985)
Douglas, R.G., Hurder, S., Kaminker, J.: Toeplitz operators and the eta invariant; the case ofS 1. In: Index theory of elliptic operators, foliations, and operator algebras. Contemp. Math.70, 11–41 (1988)
Douglas, R.G., Hurder, S., Kaminker, J.: Eta invariants and von Neumann algebras. Bull. Am. Math. Soc.,21, 83–87 (1989)
Douglas, R.G., Hurder, S., Kaminker, J.: The longitudinal cocycle and the index of Toeplitz operators. I.U.-P.U. Indianapolis, Preprint (1988)
Fegan, H.D.: The fundamental solution of the heat equation on a compact Lie group. J. Differ. Geom.18, 659–668 (1983)
Gilkey, P.B.: Invariant theory, the heat equation and the Atiyah-Singer index theorem. Publish or Perish11, 1–349 (1984)
Goodman, S., Plante, J.: Holonomy and averaging in foliated sets. J. Differ. Geom.14, 401–407 (1979)
Gromov, M., Lawson, H.B.: Positive scalar curvature and the Dirac operator. Publ. Math., Inst. Hautes Etud. Sci.,58, 83–196 (1983)
Haefliger, A.: Homotopy and integrability. In: Manifolds-Amsterdam 1970, (Lect. Notes in Math., vol. 197, pp. 133–166). Berlin Heidelberg New York: Springer 1973
Higson, N.: A primer on Kasparov'sKK-theory. University of Pennsylvania, Preprint 1988
Hurder, S.: Global invariants for measured foliations. Trans. Am. Math. Soc.280, 367–391 (1983)
Hurder, S.: Eta invariants and index theorem for coverings. Contemp. Math.105, 47–82 (1990)
Hurder, S.: Transverse index theory for self-adjoint operators. Univ. of Ill., Chicago, Preprint 1990
Hurder, S.: Analytic foliation invariants andK-theory regulators. Univ. of Ill., Chicago, Preprint 1990
Hurder, S.: Analysis and geometry of foliations. Research Monograph based on Ulam Lectures at University of Colorado, 1988–89
Jaffe, A.: Heat kernel regularization and infinite-dimensional analysis. Harvard Univ., Preprint HUTMP B-213 (December, 1987)
Jaffe, A., Lesniewski, A., Osterwalder, K.: QuantumK-Theory, I. The Chern character. Commun. Math. Phys.121, 527–540 (1989)
Kamber, F., Tondeur, Ph.: Harmonic foliations. In: Proc. NSF Conf. on Harmonic Maps. Tulane Univ., (1980), (Lect. Notes in Math., vol. 949, pp. 87–121) Berlin Heidelberg New York: Springer 1982
Kaminker, J.: Secondary invariants for elliptic operators and operator algebras. In: Operator Algebras and Applications. vol. I: Structure Theory;K-Theory, Geometry and Topology, (London Math. Soc. Lect. Notes, vol. 136, pp. 119–126). Cambridge, Cambridge Univ. Press 1988
Karoubi, M.:K-theory. An introduction. (Grundlehren der Math., Bd. 226). Berlin Heidelberg New York: Springer 1978
Kasparov, G.G.:K-functor and extension ofC *-algebras. Izv. Akad. Nauk SSSR, Ser. Mat.44, 571–636 (1980)
Lawson, H.B.: An Introduction to the Quantitative Theory of Foliations. CMBS25, 1–65 (1975)
Loday, J.-L., Quillen, D.: Cyclic homology and the Lie algebra homology of matrices. Comment. Math. Helv.59, 565–591 (1984)
Milnor, J., Stasheff, J.: Lectures on characteristic classes. Princeton: Princeton University Press 1975
Mostow, M.: Continuous cohomology of spaces with two topologies. Mem. Am. Math. Soc. 175, 1–142 (1976)
Moore, C. C., Schochet, C.: Analysis on foliated spaces. (Math. Sciences Research Inst. Publ. No. 9). Berlin Heidelberg New York: Springer 1988
Ocneanu, A.: Actions of discrete amenable groups on von Neumann algebras. (Lect. Notes in Math., vol 1138). Berlin Heidelberg New York: Springer 1985
Ocneanu, A.: Spectral theory for compact group actions. Lecture Notes, Univ. of Calif., Berkeley (May, 1985)
Plante, J.: Foliations with measure-preserving holonomy. Ann. Math.102, 327–361 (1975)
Ramachandran, M.: Cheeger-Gromov inequality for type-II eta invariants. Univ. of Colorado, Preprint (May 1989)
Reinhart, B.: Foliated manifolds with bundle-like metrics. Ann. Math.69, 119–132 (1959)
deRham, G.: Varièté diffèrentiables. Paris: Hermann (1955)
Roe, J.: An index theorem on open manifolds. I. J. Differ. Geom.27, 87–113 (1988)
Roe, J.: An index theorem on open manifolds. II. J. Differ. Geom.27, 115–136 (1988)
Roe, J.: Finite propagation speed and Connes foliation algebra. Proc. Camb. Philos. Soc.102, 459–466 (1987)
Roe, J.: Letter to S. Hurder, July 1987
Roe, J.: Elliptic operators, topology and asymptotic methods. Pitman Res. Notes Math. Ser.179, 1–177 (1988)
Ruelle, D., Sullivan, D.: Currents, flows and diffeomorphisms. Topology14, 319–327 (1975)
Sergiescu, V.: Basic cohomology and tautness of Riemannian foliations. Appendix B to “Riemannian foliations,” Molino, P. (ed.). Basel: Birkhäuser 1988
Singer, I.M.: Recent applications of index theory for elliptic operators. Proc. Symp. Pure Math.23, 11–31 (1971)
Singer, I.M.: Some remarks on operator theory and index theory. In:K-theory and Operator Algebras. Proceedings, Univ. ol Georgia 1975. (Lecture Notes in Math., vol. 575, pp. 128–138). Berlin Heidelberg New York: Springer 1977
Skandalis, G.: Une notion de nucléarité enK-Théorie.K-Theory1, 549–573 (1988)
Smagin, S.A., Ŝubin, M.A.: Zeta-function of a transversely elliptic operator. Sib. Math. J.25, 959–966 (1984)
Ŝubin, M.A.: The spectral theory and the index of elliptic operators with almost periodic coffficients. Usp. Mat. Nauk34, 95–135 (1979). English transl.: Rus. Math. Surv.34, 109–157 (1979)
Ŝubin, M.A.: Spectrum and its distribution function for a transversely elliptic operator. Funct. Anal. Appl.15, 74–76 (1981)
Taylor, M.E.: Pseudo-differential operators. Princeton: Princeton University Press 1982
Whitehead, G.W.: Elements of homotopy theory. (Graduate Texts in Mathematics, vol. 61). Berlin Heidelberg New York: Springer 1978
Wodzicki, M.: Local invariants of spectral asymmetry. Invent. Math.75, 143–178 (1984)
Wojciechowski, K.: A note on the space of pseudo-differential projections with the same principal symbol. J. Oper. Theory15, 207–216 (1986)
Vergne, M.: Sur l'indice des operateurs transversalement elliptique. C.R. Acad. Sci. Paris,310, 329–332 (1990)
Author information
Authors and Affiliations
Additional information
Oblatum 13-III-1990
Supported in part by NSF Grant DMS
Supported in part by NSF Grant DMS86-10976 and a Sloan Foundation Fellowship
Supported in part by NSF Grant DMS
Rights and permissions
About this article
Cite this article
Douglas, R.G., Hurder, S. & Kaminker, J. Cyclic cocycles, renormalization and eta-invariants. Invent Math 103, 101–179 (1991). https://doi.org/10.1007/BF01239510
Issue Date:
DOI: https://doi.org/10.1007/BF01239510