31,975 research outputs found
On non-formal simply connected manifolds
We construct examples of non-formal simply connected and compact oriented
manifolds of any dimension bigger or equal to 7.Comment: 6 pages, Latex2
Rejoinder to "Support Vector Machines with Applications"
Rejoinder to ``Support Vector Machines with Applications'' [math.ST/0612817]Comment: Published at http://dx.doi.org/10.1214/088342306000000501 in the
Statistical Science (http://www.imstat.org/sts/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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
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