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On compact symplectic and Kählerian solvmanifolds which are not completely solvable

Aleksy Tralle (1997)

Colloquium Mathematicae

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.

On G -disconnected injective models

Marek Golasiński (2003)

Annales de l’institut Fourier

Let G be a finite group. It was observed by L.S. Scull that the original definition of the equivariant minimality in the G -connected case is incorrect because of an error concerning algebraic properties. In the G -disconnected case the orbit category 𝒪 ( G ) was originally replaced by the category 𝒪 ( G , X ) with one object for each component of each fixed point simplicial subsets X H of a G -simplicial set X , for all subgroups H ⊆ G . We redefine the equivariant minimality and redevelop some results on the rational homotopy...

On the homotopy type of (n-1)-connected (3n+1)-dimensional free chain Lie algebra

Mahmoud Benkhalifa, Nabilah Abughzalah (2005)

Open Mathematics

Let R be a subring ring of Q. We reserve the symbol p for the least prime which is not a unit in R; if R ⊒Q, then p=∞. Denote by DGL nnp, n≥1, the category of (n-1)-connected np-dimensional differential graded free Lie algebras over R. In [1] D. Anick has shown that there is a reasonable concept of homotopy in the category DGL nnp. In this work we intend to answer the following two questions: Given an object (L(V), ϖ) in DGL n3n+2 and denote by S(L(V), ϖ) the class of objects homotopy equivalent...

On the real cohomology of spaces of free loops on manifolds

Katsuhiko Kuribayashi (1996)

Fundamenta Mathematicae

Let LX be the space of free loops on a simply connected manifold X. When the real cohomology of X is a tensor product of algebras generated by a single element, we determine the algebra structure of the real cohomology of LX by using the cyclic bar complex of the de Rham complex Ω(X) of X. In consequence, the algebra generators of the real cohomology of LX can be represented by differential forms on LX through Chen’s iterated integral map. Let 𝕋 be the circle group. The 𝕋 -equivariant cohomology...

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