Casson's invariant of Seifert homology 3-spheres
Casson's invariant of Seifert homology 3-spheres
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Seifert 同调 3 球体的 Casson 不变量
DOI：
10.1007/bf01446893
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发表时间：
1990
影响因子：
1.4
通讯作者：
Koichi Sakamoto
中科院分区：
文献类型：
--
作者：
S. Fukuhara;Yukio Matsumoto;Koichi Sakamoto
自从Casson [13，1]定义了他的同调3-球面的2-不变量以来，为了找到不变量的实际值，已经进行了几次尝试。Hoste [10]给出了当同调3-球面由具有某些性质的框架链环表示时计算其2-不变量的方法。Fukuhara和Maruyama [4]以及Boyer和Nicas [2]独立地证明了2-不变量的一个求和公式，它类似于Gordon的#-不变量的求和公式[6]。最近Fintushel和Stern [5]利用Floer的瞬子同调理论，成功地计算了Brieskorn同调3-球面X（a1，a2，a3）和Seifert同调3-球面X（2，3，5，7）的2-不变量。本文的目的是完全确定Seifert同调3-球面的2-不变量。
Since Casson 13, 1] defined his 2-invariant for homology 3-spheres, several attempts have been made in order to find actual values of the invariant. Hoste [10] gave a method to compute the 2-invariant for homology 3-spheres when they are presented by framed links with certain properties. Fukuhara and Maruyama [4] and Boyer and Nicas [2] proved a sum formula of 2-invariant independently which is analogous to Gordon's sum formula of the#-invariant [6]. Recently Fintushel and Stern [5], exploiting Floer's instanton homology theory, have succeeded in computing the 2-invariant of the Brieskorn homology 3-spheres X (al, a2, a3) and the Seifert homology 3-sphere X (2, 3, 5, 7). The purpose of this paper is to determine the 2-invariant of Seifert homology 3-spheres completely.