On open books for nonorientable 3-manifolds

We show that the monodromy of Klassen's genus two open book for $P^2 \times S^1$ is the $Y$-homeomorphism of Lickorish, which is also known as the crosscap slide. Similarly, we show that $S^2 \widetilde{\times} S^1$ admits a genus two open book whose monodromy is the crosscap transposition. Moreover, we show that each of $P^2 \times S^1$ and $S^2 \widetilde{\times} S^1$ admits infinitely many isomorphic genus two open books whose monodromies are mutually nonisotopic. Furthermore, we include a simple observation about the stable equivalence classes of open books for $P^2 \times S^1$ and $S^2 \widetilde{\times} S^1$. Finally, we formulate a version of Gabai's theorem about the Murasugi sum of open books, without imposing any orientability assumption on the pages.Comment: Final version, to appear in Periodica Mathematica Hungaric

Explicit horizontal open books on some Seifert fibered 3--manifolds

We describe explicit horizontal open books on some Seifert fibered 3--manifolds. We show that the contact structures compatible with these horizontal open books are Stein fillable and horizontal as well. Moreover we draw surgery diagrams for some of these contact structures.Comment: 13 page

Embedding fillings of contact 3-manifolds

In this survey article we describe different ways of embedding fillings of contact 3-manifolds into closed symplectic 4-manifolds.Comment: 25 pages, 12 figure

On the Heegaard genus of contact 3-manifolds

It is well-known that Heegaard genus is additive under connected sum of 3-manifolds. We show that 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) of 3-manifolds, and compute this invariant for some 3-manifolds