11,848 research outputs found
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
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