arXiv subjects
Publications and source records attributed to Yusuf Z. Gurtas.
A positive Dehn twist product for a $\mathbb{Z}_3$ action with $g+2$ fixed points on the 2-dimensional closed, compact, oriented surface $Σ_g$ is presented. The homeomorphism invariants of the resulting symplectic 4-manifolds are computed.
We discuss a connection between the lantern relation in mapping class groups and the rational blowing down process for 4-manifolds. More precisely, if we change a positive relator in Dehn twist generators of the mapping class group by using a lantern relation, the corresponding Lefschetz fibration changes into its rational blowdown along a copy of the configuration C_2. We exhibit examples of such rational blowdowns of Lefschetz fibrations whose blowup is homeomorphic but not diffeomorphic to the original fibration.
Positive Dehn twist products for some elements of finite order in the mapping class group of a 2-dimensional closed, compact, oriented surface $Σ_g$, which are rotations of $Σ_g$ through $2π/p$, are presented. The homeomorphism invariants of the resulting simply connected symplectic 4- manifolds are computed.