New exotic 4-manifolds via Luttinger surgery on Lefschetz fibrations
| Autor: | Kadriye Nur Saglam, Anar Akhmedov |
|---|---|
| Přispěvatelé: | Mathematics |
| Jazyk: | angličtina |
| Rok vydání: | 2015 |
| Předmět: |
Fundamental group
General Mathematics Cyclic group 0101 Pure Mathematics Combinatorics Mathematics - Geometric Topology Mathematics - Algebraic Geometry math.AG Genus (mathematics) 4-manifolds FOS: Mathematics math.GT Lefschetz fibration Algebraic Geometry (math.AG) Symplectic sum Mathematics::Symplectic Geometry Luttinger surgery Mathematics symplectic 4-manifolds exotic smooth structures math.SG SIGNATURE Fibration symplectic sum Geometric Topology (math.GT) Cohomology SMOOTH STRUCTURES LAGRANGIAN TORI Mathematics - Symplectic Geometry Free group Symplectic Geometry (math.SG) Symplectic geometry |
| Popis: | In [2], the first author constructed the first known examples of exotic minimal symplectic $\CP#5\CPb$ and minimal symplectic 4-manifold that is homeomorphic but not diffeomorphic to $3\CP#7\CPb$. The construction in [2] uses Y. Matsumoto's genus two Lefschetz fibrations on $M = \mathbb{T}^{2}\times \mathbb{S}^{2} #4\CPb$ over $\mathbb{S}^2$ along with the fake symplectic $\mathbb{S}^{2} \times \mathbb{S}^{2}$ construction given in [1]. The main goal in this paper is to generalize the construction in [2] using the higher genus versions of Matsumoto's fibration constructed by Mustafa Korkmaz and Yusuf Gurtas on $M(k,n) = \Sigma_{k}\times \mathbb{S}^{2} #4n\CPb$ for any $k \geq 2$ and $n = 1$, and $k \geq 1$ and $n \geq 2$, respectively. Using our building blocks, we also construct symplectic 4-manifolds with the free group of rank $s \geq 1$ and various other finitely generated groups as the fundamental group. Comment: 21 pages, 7 figures. One reference added, a few extra clarifying comments added |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|