Formality and the Lefschetz property in symplectic and cosymplectic geometry
نویسندگان
چکیده
We review topological properties of Kähler and symplecticmanifolds, and of their odd-dimensional counterparts, coKähler and cosymplectic manifolds. We focus on formality, Lefschetz property and parity of Betti numbers, also distinguishing the simply-connected case (in the Kähler/symplectic situation) and the b1 = 1 case (in the coKähler/cosymplectic situation). MSC: 53C15, 55S30, 53D35, 55P62, 57R17.
منابع مشابه
On the formality and the hard Lefschetz property for Donaldson symplectic manifolds
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 Donaldson symplectic manifolds constructed in [13]. This study permits us to show an example of a Donaldson symplectic manifol...
متن کاملFormality 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 Donaldson submanifolds of symplectic manifolds constructed in [13]. This study permits us to show an example of a Donaldson sym...
متن کامل2 D ec 2 00 4 FORMALITY IN 7 AND 8 DIMENSIONS GIL
Using the concept of s-formality we are able to extend the bounds of a Theorem of Miller and show that a compact k-connected 4k + 3or 4k + 4-manifold with bk+1 = 1 is formal. We study simply-connected 7and 8-manifolds with a hard Lefschetz-like property and prove that in this case if b2 = 2, then the manifold is formal, while, in 7-dimensions, if b2 = 3 all Massey products vanish. We finish wit...
متن کاملdG, δ-LEMMA FOR EQUIVARIANT DIFFERENTIAL FORMS WITH GENERALIZED COEFFICIENT
Consider a Hamiltonian action of a compact Lie Group on a symplectic manifold which has the strong Lefschetz property. We establish an equivariant version of the Merkulov-Guillemin dδ-lemma for equivariant differential forms with smooth or distributional coefficient. As a corollary we also obtain a version of equivariant formality theorem in this case.
متن کاملCohomologically Kähler Manifolds with No Kähler Metrics
We show some examples of compact symplectic solvmanifolds, of dimension greater than four, which are cohomologically Kähler and do not admit Kähler metric since their fundamental groups cannot be the fundamental group of any compact Kähler manifold. Some of the examples that we study were considered by Benson and Gordon (1990). However, whether such manifolds have Kähler metrics was an open que...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2015