当前位置: X-MOL 学术Compos. Math. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Rigidity of the mod 2 families Seiberg–Witten invariants and topology of families of spin 4-manifolds
Compositio Mathematica ( IF 1.3 ) Pub Date : 2021-04-15 , DOI: 10.1112/s0010437x2000771x
Tsuyoshi Kato , Hokuto Konno , Nobuhiro Nakamura

We show a rigidity theorem for the Seiberg–Witten invariants mod 2 for families of spin 4-manifolds. A mechanism of this rigidity theorem also gives a family version of 10/8-type inequality. As an application, we prove the existence of non-smoothable topological families of 4-manifolds whose fiber, base space, and total space are smoothable as manifolds. These non-smoothable topological families provide new examples of $4$-manifolds $M$ for which the inclusion maps $\operatorname {Diff}(M) \hookrightarrow \operatorname {Homeo}(M)$ are not weak homotopy equivalences. We shall also give a new series of non-smoothable topological actions on some spin $4$-manifolds.



中文翻译:

mod 2族Seiberg–Witten不变量的刚性和自旋4流形族的拓扑

我们显示了自旋4流形族的Seiberg-Witten不变量mod 2的刚性定理。该刚性定理的机制还给出了10/8型不等式的族形式。作为一个应用,我们证明了4流形的非光滑拓扑族的存在,这些流形的纤维,基础空间和总空间可以作为流形平滑。这些不可平滑的拓扑族提供了$ 4 $-流形$ M $的新示例,对于这些示例,包含映射$ \ operatorname {Diff}(M)\ hookrightarrow \ operatorname {Homeo}(M)$并不是弱的同伦等价物。我们还将对某些旋转的$ 4 $流形给出一系列新的不平滑拓扑动作。

更新日期:2021-04-15
down
wechat
bug