The E8-boundings of homology spheres and negative sphere classes in E(1)
The E8-boundings of homology spheres and negative sphere classes in E(1)
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E(1) 中同源球和负球类的 E8 界
DOI：
10.1016/j.topol.2015.12.067
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发表时间：
2016
影响因子：
0.6
通讯作者：
Motoo Tange
中科院分区：
文献类型：
--
作者：
Tetsuya Abe;Motoo Tange;Motoo Tange;Motoo Tange;Motoo Tange
我们定义了同调3球的拓扑不变量ds和ds _，它们是同调球的确定自旋界中的最大和最小秒贝蒂数除以8。我们还用边界4流形的二次型e8的极大（或极小）积和定义了相似的不变量g8和g8_。这些不变量的目的是测量边界确定自旋4流形的大小。给出了几种构造确定自旋边界的方法。特别地，我们利用柄分解构造了Σ （2,3,12 n+ 5）的不常见的e8界。作为这种构造的副产品，我们证明了E(1)中的某些负的第2同调类k [f]−[s]用一个球表示，其中f和s是E(1)的纤维和截面类。
We define topological invariants of homology 3-sphere, ds and ds _, which are the maximal and minimal second Betti number divided by 8 among definite spin boundings of the homology sphere. We also define similar invariants g 8 and g 8 _ by the maximal (or minimal) product sum of the quadratic form E 8 of bounding 4-manifolds. The aim of these invariants is to measure the size of bounding definite spin 4-manifold. We give several ways to construct definite spin boundings. In particular, we construct uncommon E 8-boundings for Σ (2, 3, 12 n+ 5) by using handle decomposition. As a by-product of this construction, we show that some negative 2nd homology classes k [f]−[s] in E (1) are represented by a sphere, where f and s are a fiber and sectional class of E (1).