Free group automorphisms and knotted tori in S-4

被引:3
|
作者
Silver, DS
机构
[1] Dept. of Mathematics and Statistics, University of South Alabama, Mobile
关键词
2-knot; torus P-knot; pseudo-Anosov monodromy;
D O I
10.1142/S021821659700008X
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Let phi be an automorphism of a finitely generated free group F, omega and element of F, and H the subgroup of F generated by the orbit {phi(n)(omega), \n is an element of Z}. We describe sufficient conditions ensuring that H is non-finitely generated. Using this we give a simple construction of tori T embedded in S-4 in such a way that the commutator subgroup of pi(1)(S-4 - T) is finitely generated but not finitely presented. Such tori have no minimal Seifert manifolds. An example of an embedded torus with the latter property was given recently by T. Maeda using different methods.
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页码:95 / 103
页数:9
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