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1994 | 145 | 2 | 181-204
Tytuł artykułu

Cohomology of some graded differential algebras

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We study cohomology algebras of graded differential algebras which are models for Hochschild homology of some classes of topological spaces (e.g. homogeneous spaces of compact Lie groups). Explicit formulae are obtained. Some applications to cyclic homology are given.
Słowa kluczowe
Rocznik
Tom
145
Numer
2
Strony
181-204
Opis fizyczny
Daty
wydano
1994
otrzymano
1993-08-24
poprawiono
1994-01-06
Twórcy
  • Institute of Mathematics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin 3, Poland
  • Institute of Mathematics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin 3, Poland, trallemt@plszus11.bitnet
Bibliografia
  • [1] A. Borel, Sur la cohomologie des espaces fibrés principaux et des espaces homogènes de groupes de Lie compacts, Ann. of Math. 57 (1953), 115-207.
  • [2] D. Burghelea, Cyclic homology and the algebraic K-theory of spaces I, in: Contemp. Math. 55, Amer. Math. Soc., 1986, 89-115.
  • [3] D. Burghelea and Z. Fiedorowicz, Cyclic homology and algebraic K-theory of spaces - II, Topology 25 (1986), 303-317.
  • [4] D. Burghelea and M. Vigué-Poirrier, Cyclic homology of commutative algebras I, in: Lecture Notes in Math. 1318, Springer, 1988, 51-72.
  • [5] A. Connes and H. Moscovici, Cyclic cohomology, the Novikov conjecture and hyperbolic groups, Topology 29 (1990), 345-388.
  • [6] L. Flatto, Invariants of reflection groups, Enseign. Math. 24 (1978), 237-293.
  • [7] T. Goodwillie, Cyclic homology, derivations, and the free loop space, Topology 24 (1985), 187-215.
  • [8] V. Greub, S. Halperin and R. Vanstone, Curvature, Connections and Cohomology, Vol. 3, Academic Press, New York, 1976.
  • [9] J. A. Guccione, J. J. Guccione, M. J. Redondo and O. R. Villamayor, Hochschild and cyclic homology of hypersurfaces, Adv. in Math. 95 (1992), 18-60.
  • [10] S. Halperin and M. Vigué-Poirrier, The homology of a free loop space, Pacific J. Math. 147 (1991), 311-324.
  • [11] E. Kunz, Introduction to Commutative Algebra and Algebraic Geometry, Birkhäuser, 1985.
  • [12] A. Lago and A. Rodicio, Generalized Koszul complexes and Hochschild (co-)homology of complete intersections, Invent. Math. 107 (1992), 433-446.
  • [13] D. Lehmann, Théorie homotopique des formes différentielles (d'après D. Sullivan), Astérisque 45 (1977).
  • [14] J. L. Loday, Cyclic Homology, Springer, 1992.
  • [15] J. McCleary, User's Guide to Spectral Sequences, Publish or Perish, 1985.
  • [16] A. Tralle, Cyclic homology of some topological spaces which are formal in the sense of Sullivan, Mat. Zametki 50 (6) (1991), 131-141 (in Russian).
  • [17] A. Tralle, On Hochschild and cyclic homology of certain homogeneous spaces, Czechoslovak Math. J. 43 (1993), 615-634.
  • [18] M. Vigué-Poirrier, Homologie cyclique des espaces formels, J. Pure Appl. Algebra, to appear.
  • [19] M. Vigué-Poirrier and D. Burghelea, A model for cyclic homology and algebraic K-theory of 1-connected topological spaces, J. Differential Geom. 22 (1985), 243-253.
  • [20] M. Vigué-Poirrier and D. Sullivan, The homology theory of the closed geodesic problem, ibid. 11 (1976), 633-644.
  • [21] E. Witten, The index of the Dirac operator in loop space, in: Lecture Notes in Math. 1326, Springer, 1988, 161-181.
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Bibliografia
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bwmeta1.element.bwnjournal-article-fmv145i2p181bwm
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