The Generalized Smith Conjecture of Codimension Greater Than Two
The Generalized Smith Conjecture of Codimension Greater Than Two
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余维大于二的广义史密斯猜想
DOI：
10.1142/s0218216500000256
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发表时间：
2000
影响因子：
0.5
通讯作者：
Zhi Lü
中科院分区：
文献类型：
--
作者：
Zhi Lü
本文考虑余维大于2的广义Smith猜想，即如果L-h>；2和h>；3，则S1的任何周期变换都不能有驯服的纽结Sh作为不动点集。本文利用Brieskorn球面，给出了如下情形的显式反例：(I)L-h是偶数，而L是奇数；(Ii)2l≤3(h+1)和h+1≡0(Mod 4)。
In this paper we consider the generalized Smith conjecture of codimension greater than two, which says that no periodic tranformation of Sl can have the tame knotted Sh as fixed point set if l-h>2 and h>3. Using the Brieskorn spheres, this paper gives the explicit counterexamples to show that the conjecture is false in the DIFF category for the following cases: (i) l-h is even more than 2 and l is odd; (ii) 2l≤3(h+1) and h+1≡0 (mod 4).