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On the Heegaard genus of contact 3-manifolds

100%
Ozbagci B.
Open Mathematics
|
2011
|
tom 9
|
nr 4
752-756
EN
It is well-known that the Heegaard genus is additive under connected sum of 3-manifolds. We show that the Heegaard genus of contact 3-manifolds is not necessarily additive under contact connected sum. We also prove some basic properties of the contact genus (a.k.a. open book genus [Rubinstein J.H., Comparing open book and Heegaard decompositions of 3-manifolds, Turkish J. Math., 2003, 27(1), 189–196]) of 3-manifolds, and compute this invariant for some 3-manifolds.
2
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Homological Mirror Symmetry for manifolds of general type

61%
Kapustin A., Katzarkov L., Orlov D., Yotov M.
Open Mathematics
|
2009
|
tom 7
|
nr 4
571-605
EN
In this paper we outline the foundations of Homological Mirror Symmetry for manifolds of general type. Both Physics and Categorical prospectives are considered.
3
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Formality and the Lefschetz property in symplectic and cosymplectic geometry

52%
Bazzoni G., Fernández M., Muñoz V.
Complex Manifolds
|
2015
|
tom 2
|
nr 1
EN
We review topological properties of Kähler and symplectic manifolds, 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).
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