1,200 research outputs found
Simply-connected K-contact and Sasakian manifolds of dimension 7
We construct a compact simply-connected 7-dimensional manifold admitting a
K-contact structure but not a Sasakian structure. We also study rational
homotopy properties of such manifolds, proving in particular that a
simply-connected 7-dimensional Sasakian manifold has vanishing cup-product on
the second cohomology and that it is formal if and only if all its triple
Massey products vanish.Comment: 14 pages, some references added, several typos are correcte
Weakly Lefschetz symplectic manifolds
The harmonic cohomology of a Donaldson symplectic submanifold and of an
Auroux symplectic submanifold are compared with that of its ambient space. We
also study symplectic manifolds satisfying a weakly Lefschetz property, that
is, the -Lefschetz propery. In particular, we consider the symplectic
blow-ups of the complex projective space along weakly Lefschetz symplectic
submanifolds. As an application we construct, for each even integer ,
compact symplectic manifolds which are -Lefschetz but not -Lefschetz.Comment: 22 pages; many improvements from previous versio
Symplectic resolutions, Lefschetz property and formality
We introduce a method to resolve a symplectic orbifold into a smooth
symplectic manifold. Then we study how the formality and the Lefschetz property
of the symplectic resolution are compared with that of the symplectic orbifold.
We also study the formality of the symplectic blow-up of a symplectic orbifold
along symplectic submanifolds disjoint from the orbifold singularities. This
allows us to construct the first example of a simply connected compact
symplectic manifold of dimension 8 which satisfies the Lefschetz property but
is not formal, therefore giving a counter-example to a conjecture of Babenko
and Taimanov.Comment: 21 pages, no figure
Spin-harmonic structures and nilmanifolds
We introduce spin-harmonic structures, a class of geometric structures on
Riemannian manifolds of low dimension which are defined by a harmonic unitary
spinor. Such structures are related to SU(2) (dim=4,5), SU(3) (dim=6) and G_2
(dim=7) structures; in dimension 8, a spin-harmonic structure is equivalent to
a balanced Spin(7) structure. As an application, we obtain examples of compact
8-manifolds endowed with non-integrable Spin(7) structures of balanced type.Comment: 34 pages, no figure
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