13,881 research outputs found
Formality of Donaldson submanifolds
We introduce the concept of s-formal minimal model as an extension of
formality. We prove that any orientable compact manifold M, of dimension 2n or
(2n-1), is formal if and only if M is (n-1)-formal. The formality and the hard
Lefschetz property are studied for the symplectic manifolds constructed by
Donaldson with asymptotically holomorphic techniques. This study permits us to
show an example of a Donaldson symplectic manifold of dimension eight which is
formal simply connected and does not satisfy the hard Lefschetz theorem.Comment: 24 pages, no figures, Latex2e; v3. statement of Lemma 2.7 correcte
An 8-dimensional non-formal simply connected symplectic manifold
A non-formal simply connected compact symplectic manifold of dimension 8 is
constructed.Comment: 8 pages, 1 figure; v2. exposition greatly improved; v3. final
version. To appear in Annals of Mathematic
Formality and the Lefschetz property in symplectic and cosymplectic geometry
We review topological properties of K\"ahler and symplectic manifolds, and of
their odd-dimensional counterparts, coK\"ahler and cosymplectic manifolds. We
focus on formality, Lefschetz property and parity of Betti numbers, also
distinguishing the simply-connected case (in the K\"ahler/symplectic situation)
and the case (in the coK\"ahler/cosymplectic situation).Comment: 27 pages, no figures. Comments are welcome
Non-formal co-symplectic manifolds
We study the formality of the mapping torus of an orientation-preserving
diffeomorphism of a manifold. In particular, we give conditions under which a
mapping torus has a non-zero Massey product. As an application we prove that
there are non-formal compact co-symplectic manifolds of dimension and with
first Betti number if and only if and , or and
. Explicit examples for each one of these cases are given.Comment: Only minor changes with respect to version 1 (some terminology
clarified). 21 pages, no figures. To appear in Trans. Am. Math. So
On formality of Sasakian manifolds
We investigate some topological properties, in particular formality, of
compact Sasakian manifolds. Answering some questions raised by Boyer and
Galicki, we prove that all higher (than three) Massey products on any compact
Sasakian manifold vanish. Hence, higher Massey products do obstruct Sasakian
structures. Using this we produce a method of constructing simply connected
K-contact non-Sasakian manifolds. On the other hand, for every , we
exhibit the first examples of simply connected compact Sasakian manifolds of
dimension which are non-formal. They are non-formal because they have
a non-zero triple Massey product. We also prove that arithmetic lattices in
some simple Lie groups cannot be the fundamental group of a compact Sasakian
manifold.Comment: 22 pages, no figures; v2. some corrections; v3. Accepted in J.
Topolog
Nearly hypo structures and compact Nearly K\"ahler 6-manifolds with conical singularities
We prove that any totally geodesic hypersurface of a 6-dimensional
nearly K\"ahler manifold is a Sasaki-Einstein manifold, and so it has a
hypo structure in the sense of \cite{ConS}. We show that any Sasaki-Einstein
5-manifold defines a nearly K\"ahler structure on the sin-cone
, and a compact nearly K\"ahler structure with conical
singularities on when is compact thus providing a
link between Calabi-Yau structure on the cone and the
nearly K\"ahler structure on the sin-cone . We define the
notion of {\it nearly hypo} structure that leads to a general construction of
nearly K\"ahler structure on . We determine {\it double
hypo} structure as the intersection of hypo and nearly hypo structures and
classify double hypo structures on 5-dimensional Lie algebras with non-zero
first Betti number. An extension of the concept of nearly K\"ahler structure is
introduced, which we refer to as {\it nearly half flat} SU(3)-structure, that
leads us to generalize the construction of nearly parallel -structures on
given in \cite{BM}. For and for
, we describe explicitly a
Sasaki-Einstein hypo structure as well as the corresponding nearly K\"ahler
structures on and , and the nearly
parallel -structures on and .Comment: 28 pages, new four figures, references added, final version to appear
in the Journal of the London. Math. So
Resistance to the SDHI fungicides boscalid and fluopyram in Podosphaera xanthii from commercial cucurbit fields in Spain
Powdery mildew elicited by Podosphaera xanthii is a devastating disease of cucurbits worldwide and one of the most important diseases affecting these crops in Spain. Application of fungicides is the main control practice for managing P. xanthii; however, isolates resistant to multiple classes of site-specific fungicides have been recently reported in the Spanish cucurbit powdery mildew population. Succinate dehydrogenase inhibitors (SDHIs) constitute a relatively novel class of fungicides registered for powdery mildew control representing new alternatives for cucurbit growers. In the present study, 30 P. xanthii isolates were used to determine the effective concentration that reduces mycelial growth by 50% (EC50) to boscalid and fluopyram. The present study was also conducted to obtain discriminatory doses to monitor SDHI fungicide resistance in 180 P. xanthii isolates collected from several commercial cucurbit fields in Spain during 2017-2018. Three SDHI resistance patterns were observed in our population, which include patterns I (resistance to boscalid), II (resistance to fluopyram), and III (resistance to boscalid and fluopyram). The amino acid changes associated with these resistance patterns in the Sdh protein were also examined. Based on our results, SDHI fungicides are good alternatives for cucurbit powdery mildew control, although they should be applied with caution.Universidad de Málaga. Campus de Excelencia Internacional AndalucĂa Tec
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