Rational formality of function spaces.
Vigué-Poirrier, Micheline (2007)
Journal of Homotopy and Related Structures
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Vigué-Poirrier, Micheline (2007)
Journal of Homotopy and Related Structures
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Dupont, Nicolas, Hess, Kathryn (2002)
Homology, Homotopy and Applications
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Barmak, Jonathan Ariel, Minian, Elias Gabriel (2007)
Journal of Homotopy and Related Structures
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Johansson, Leif, Lambe, Larry, Sköldberg, Emil (2002)
Homology, Homotopy and Applications
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Gregory Lupton (1998)
Banach Center Publications
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Halperin has conjectured that the Serre spectral sequence of any fibration that has fibre space a certain kind of elliptic space should collapse at the -term. In this paper we obtain an equivalent phrasing of this conjecture, in terms of formality relations between base and total spaces in such a fibration (Theorem 3.4). Also, we obtain results on relations between various numerical invariants of the base, total and fibre spaces in these fibrations. Some of our results give weak versions...
Martin Arkowitz (1998)
Banach Center Publications
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We give conditions for a map of spaces to induce maps of the homology decompositions of the spaces which are compatible with the homology sections and dual Postnikov invariants. Several applications of this result are obtained. We show how the homotopy type of the (n+1)st homology section depends on the homotopy type of the nth homology section and the (n+1)st homology group. We prove that all homology sections of a co-H-space are co-H-spaces, all n-equivalences of the homology decomposition...
Urtzi Buijs, Aniceto Murillo (2006)
Annales de l’institut Fourier
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Via the Bousfield-Gugenheim realization functor, and starting from the Brown-Szczarba model of a function space, we give a functorial framework to describe basic objects and maps concerning the rational homotopy type of function spaces and its path components.
Ndombol, Bitjong (2005)
AMA. Algebra Montpellier Announcements [electronic only]
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Shiga, Hiroo, Yamaguchi, Toshihiro (2003)
Homology, Homotopy and Applications
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Katsuya Eda, Kazuhiro Kawamura (2000)
Fundamenta Mathematicae
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For the n-dimensional Hawaiian earring n ≥ 2, and is trivial for each 1 ≤ i ≤ n - 1. Let CX be the cone over a space X and CX ∨ CY be the one-point union with two points of the base spaces X and Y being identified to a point. Then for n ≥ 1.
Aleksy Tralle (1997)
Colloquium Mathematicae
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We are interested in the problem of describing compact solvmanifolds admitting symplectic and Kählerian structures. This was first considered in [3, 4] and [7]. These papers used the Hattori theorem concerning the cohomology of solvmanifolds hence the results obtained covered only the completely solvable case}. Our results do not use the assumption of complete solvability. We apply our methods to construct a new example of a compact symplectic non-Kählerian solvmanifold.