On Hochschild and cyclic homology of certain homogeneous spaces

Tralle, Aleksei E.

Czechoslovak Mathematical Journal, Tome 43 (1993) no. 4, pp. 615-634

Détail

DOI : 10.21136/CMJ.1993.128437

Classification : 19D55, 55N91, 55P62

Bibliographie

[1] J. M. Boardman, R. M. Vogt: Homotopy invariant algebraic structures on topological spaces. LNM, no. 347, Berlin-Heidelberg-New York, 1973. | MR

[2] A. Borel: Sur la cohomologie des espaces fibres principaux et des espaces homogenes de groupes de Lie compacts. Annals of Math. 57 (1953), 115–207. | DOI | MR | Zbl

[3] A. Borel, F. Hirzebruch: Characteristic classes and homogeneous spaces 1. Amer. J. Math. 80 (1958), 459–538. | MR

[4] A. K. Bousfield, V. K. A. M. Guggenheim: On PL de Rham theory and rational homotopy type. Memoirs Amer. Math. Soc. 8(179) (1976). | MR

[5] D. Burghelea: Cyclic homology and the algebraic $K$-theory of spaces 1. Contemp. Math. 55 (1986), 89–115. | MR

[6] D. Burghelea, Z. Fiedorowicz: Cyclic homology and algebraic $K$-theory of spaces 2. Topology 25 (1986), 303–317. | DOI | MR

[7] A. Connes: De Rham homology and non-commutative algebra. Publ. Math. IHES 62 (1985), 94–144.

[8] A. Connes: Cohomologie cyclique et founkteur Ext$^n$. C. r. Acad. Sci. Paris, Ser. A 296 (1983), 953–958. | MR

[9] A. Connes, H. Moscovici: Cyclic homology, the Novikov conjecture and hyperbolic groups. Topology 29 (1990), 345–388. | DOI | MR

[10] K. Doan: Poicaré polynomials of compact homogeneous Riemannian spaces with irreducible isotropy subgroup. Trudy Semin. Vect. Tens. Anal. 14 (1968), 33–93. (Russian) | MR

[11] M. El-Hauari: Cohomologie de Hochschild et $k$-formalite intrinseque. C. r. Acad. Sci. Paris, Ser. 1 310 (1990), 731–734. | MR

[12] T. Goodwillie: Cyclic homology, derivations and the free loop space. Topology 24 (1985), 187–215. | DOI | MR

[13] V. Greub, S. Halperin, R. Vanstone: Curvature, connections and cohomology, v. 3. Academic Press, New York, 1976.

[14] P. Griffiths, J. Morgan: Rational homotopy theory and differential forms. Birkhäuser, Boston, 1981. | MR

[15] S. Halperin, M. Vigué-Poirrier: The homology of a free loop space. Pacif. J. Math. 147 (1991), 311–324. | DOI | MR

[16] M.-C. Heidemann-Tcherkez, M. Vigué-Poirrier: Application de la theorie des polynomes de Hilbert-Samuel a l’etude de certaines algebres differentielles. C. r. Acad. Sci. Paris, Ser. A 278 (1974), 1607–1610. | MR

[17] S. Helgason: Differential Geometry, Lie Groups and Symmetric Spaces. Academic Press, New York, 1978. | MR | Zbl

[18] Y. Kihoon: Almost complex homogeneous spaces and their submanifolds. World Scientific, Singapoor, 1987. | MR

[19] R. Krasauskas: Certain topological applications of dyhedral homology. Ph.D. Thesis, Moscow University, 1987. (Russian)

[20] D. Lehmann: Theorie homotopique des formes differentielles (d’apres D. Sullivan). Societe mathematique de France, Asterisque 45 (1977). | MR

[21] P. Rashevskii: On real cohomology of homogeneous spaces. Uspekhi Mat. Nauk 24(3) (1969), 23–90. (Russian)

[22] M. Vigué-Poirrier, D. Burghelea: A model for cyclic homology and algebraic $K$-theory of 1-connected topological spaces. J. Diff. Geom. 22 (1985), 243–253. | DOI | MR

[23] M. Vigué-Poirrier, D. Burghelea: Cyclic homology of commutative algebras. Publ. IRMA–Lille 8(1) (1987).

[24] M. Vigué-Poirrier: Cyclic homology of algebraic hypersurfaces. Publ. IRMA–Lille 10(7) (1987).

[25] M. Vigué-Poirrier: Cyclic homology and Quillen homology of a commutative algebra. Publ. IRMA–Lille 5(1) (1986).

[26] M. Vigué-Poirrier: Homologie de Hochschild et homologie cyclique des algebres differentielles graduees. Publ. IRMA–Lille 17(1) (1989). | MR

[27] E. Witten: The index of a Dirac operator in loop space. LNM, no. 1326, 1986, pp. 161–181. | MR

[28] A. E. Tralle: Cyclic homology of certain topological spaces which are formal in the sense of Sullivan. Matem. Zametki 50(6) (1991), 131–141, English transl. in “Math. Notes”. (Russian) | MR