Noncomplex smooth 4-manifolds with Lefschetz fibrations

For every integer g greater than or equal to 2, there exist infinitely many pairwise nonhomeomorphic smooth 4-manifolds that admit genus-g Lefschetz fibrations over S^2 but do not carry any complex structure with either orientation. This extends a recent result of Ozbagci and Stipsicz.Comment: 14 pages, 4 figure

Stable commutator length of a Dehn twist

It is proved that the stable commutator length of a Dehn twist in the mapping class group is positive and the tenth power of a Dehn twist about a nonseparating simple closed curve is a product of two commutators. As an application a new proof of the fact that the growth rate of a Dehn twist is linear is given.Comment: Title and the content have been changed. The last part of the previous version is included in another paper. Now the paper is 10 pages with no pictures. New abstract. To appear in Michigan Math. Journa