论文标题
属 - $ 3 $ lefschetz纤维和异国情调$ 4 $ -Manifolds，带有$ b_ {2}^{+} = 3 $
Genus-$3$ Lefschetz Fibrations and Exotic $4$-Manifolds with $b_{2}^{+}=3$
论文作者
论文摘要
我们明确构建了一个属 - $ 3 $ lefschetz纤维纤维，超过$ \ mathbb {s}^{2} $，其总空间为$ \ MATHBB {t}^{2} \ times \ times \ times \ times \ mathbb {s}^{2}^{2} {2} \＃6 \＃6 \＃6 \＃6 \ MATHBBBB}松本的属 - $ 2 $ lefschetz纤维化。然后，我们构建更多属 - $ 3 $ lefschetz纤维纤维，其总空间是异国情调的最小符号$ 4 $ -MANIFOLDS $ 3 \ MATHBB {C} p^{2} \＃Q \ Q \ Q \ Q \ overline {\ Mathbb {c}我们还概括了我们的构造，以获得属 - $ 3K $ lefschetz纤维化结构，$ 4 $ -MANIFOLD $σ_{K} \ times \ times \ Mathbb {s}^{2}^{2} \＃6 \ 6 \ 6 \ overline {\ Mathbb {c} p} p} p^{2} $ 2k $ 2-振动。从这个通用版本中，我们通过Luttinger手术和扭曲的纤维和进一步的奇异$ 4 $ - manifolds。
We explicitly construct a genus-$3$ Lefschetz fibration over $\mathbb{S}^{2}$ whose total space is $\mathbb{T}^{2}\times \mathbb{S}^{2}\# 6\overline{\mathbb{C} P^{2}}$ using the monodromy of Matsumoto's genus-$2$ Lefschetz fibration. We then construct more genus-$3$ Lefschetz fibrations whose total spaces are exotic minimal symplectic $4$-manifolds $3 \mathbb{C} P^{2} \# q\overline{\mathbb{C} P^{2}}$ for $q=13,\ldots,19$. We also generalize our construction to get genus-$3k$ Lefschetz fibration structure on the $4$-manifold $Σ_{k}\times \mathbb{S}^{2}\# 6\overline{\mathbb{C} P^{2}}$ using the generalized Matsumoto's genus-$2k$ Lefschetz fibration. From this generalized version, we derive further exotic $4$-manifolds via Luttinger surgery and twisted fiber sum.
