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## Fundamenta Mathematicae

1997 | 154 | 1 | 57-73
Tytuł artykułu

### The cohomology algebra of certain free loop spaces

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let X be a simply connected space and LX the space of free loops on X. We determine the mod p cohomology algebra of LX when the mod p cohomology of X is generated by one element or is an exterior algebra on two generators. We also provide lower bounds on the dimensions of the Hodge decomposition factors of the rational cohomology of LX when the rational cohomology of X is a graded complete intersection algebra. The key to both of these results is the identification of an important subalgebra of the Hochschild homology of a graded complete intersection algebra over a field.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
57-73
Opis fizyczny
Daty
wydano
1997
otrzymano
1996-05-23
poprawiono
1997-01-21
poprawiono
1997-04-14
Twórcy
autor
• Graduate School of Science and Technology, Okayama University, Okayama 700, Japan, t_yama@math.okayama-u.ac.jp
• Department of Applied Mathematics, Okayama University of Science, 1-1 Ridai-cho, Okayama 700, Japan
• Department of Applied Mathematics, Okayama University of Science, 1-1 Ridai-cho, Okayama 700, Japan, kuri@geom.xmath.ous.ac.jp
• Graduate School of Science and Technology, Okayama University, Okayama 700, Japan
Bibliografia
• [1] W. Andrzejewski and A. Tralle, Cohomology of some graded differential algebras, Fund. Math. 145 (1994), 181-204.
• [2] D. Anick, Connections between Yoneda and Pontrjagin algebras, in: Lecture Notes in Math. 1051, Springer, 1984, 331-350.
• [3] D. Burghelea, Z. Fiedorowicz and W. Gajda, Adams operations in Hochschild and cyclic homology of de Rham algebra and free loop spaces, K-Theory 4 (1991), 269-287.
• [4] D. Burghelea and M. Vigué-Poirrier, Cyclic homology of commutative algebras I, in: Lecture Notes in Math. 1318, Springer, 1988, 51-72.
• [5] S. Eilenberg and J. C. Moore, Homology and fibrations, Comment. Math. Helv. 40 (1966), 199-236.
• [6] M. El Haouari, p-Formalité des espaces, J. Pure Appl. Algebra 78 (1992), 27-47.
• [7] E. Getzler and J. D. S. Jones, $A_∞$-algebras and the cyclic bar complex, Illinois J. Math. 34 (1990), 256-283.
• [8] E. Getzler, J. D. S. Jones and S. Petrack, Differential forms on loop spaces and the cyclic bar complex, Topology 30 (1991), 339-371.
• [9] S. Halperin and J. Stasheff, Obstructions to homotopy equivalences, Adv. Math. 32 (1979), 233-279.
• [10] S. Halperin and M. Vigué-Poirrier, The homology of a free loop space, Pacific J. Math. 147 (1991), 311-324.
• [11] K. Kuribayashi, On the mod p cohomology of the spaces of free loops on the Grassmann and Stiefel manifolds, J. Math. Soc. Japan 43 (1991), 331-346.
• [12] RD. L. Rector, Steenrod operations in the Eilenberg-Moore spectral sequence, Comment. Math. Helv. 45 (1970), 540-552.
• [13] L. Smith, Homological algebra and the Eilenberg-Moore spectral sequence, Trans. Amer. Math. Soc. 129 (1967), 58-93.
• [14] L. Smith, On the Künneth theorem I, Math. Z. 166 (1970), 94-140.
• [15] L. Smith, On the characteristic zero cohomology of the free loop space, Amer. J. Math. 103 (1981), 887-910.
• [16] L. Smith, A note on the realization of graded complete intersection algebras by the cohomology of a space, Quart. J. Math. Oxford Ser. (2) 33 (1982), 379-384.
• [17] L. Smith, The Eilenberg-Moore spectral sequence and the mod 2 cohomology of certain free loop spaces, Illinois J. Math. 28 (1984), 516-522.
• [18] 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.
• [19] M. Vigué-Poirrier and D. Sullivan, The homology theory of the closed geodesic problem, J. Differential Geom. 11 (1976), 633-644.
Typ dokumentu
Bibliografia
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