Unique fiber sum decomposability of genus 2 Lefschetz fibrations
Abstract
By applying the lantern relation substitutions to the positive relation of the genus two Lefschetz fibration over $\mathbb{S}^{2}$. We show that $K3\#2 \overline{\mathbb{CP}}{}^{2}$ can be rationally blown down along seven disjoint copies of the configuration $C_2$. We compute the SeibergWitten invariant of the resulting symplectic 4manifolds, and show that they are symplectically minimal. We also investigate how these exotic smooth 4manifolds constructed via lantern relation substitution method are fiber sum decomposable. Furthermore by considering all the possible decompositions for each of our decomposable exotic examples, we will find out that there is a uniquely decomposing genus 2 Lefschetz fibration which is not a self sum of the same fibration up to diffeomorphism on the indecomposable summands.
 Publication:

arXiv eprints
 Pub Date:
 July 2015
 arXiv:
 arXiv:1507.04041
 Bibcode:
 2015arXiv150704041P
 Keywords:

 Mathematics  Geometric Topology;
 Mathematics  Symplectic Geometry
 EPrint:
 28 pages, 9 color figures