Markov's theorem in 3-manifolds

被引：53

作者：

Lambropoulou, S

Rourke, CP

机构：

[1] UNIV GOTTINGEN,MATH INST,D-37073 GOTTINGEN,GERMANY

[2] UNIV CAMBRIDGE,DPMMS,CAMBRIDGE CB2 1SB,ENGLAND

[3] UNIV WARWICK,INST MATH,COVENTRY CV4 7AL,W MIDLANDS,ENGLAND

来源：

TOPOLOGY AND ITS APPLICATIONS | 1997年 / 78卷 / 1-2期

关键词：

knot; link; isotopy; braid; Markov equivalence; L-move; knot complement; mixed diagram; 3-manifold; band move;

D O I：

10.1016/S0166-8641(96)00151-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we first give a one-move version of Markov's braid theorem for knot isotopy in S-3 that sharpens the classical theorem. Then we give a relative version of Markov's theorem concerning a fixed braided portion in the knot. We also prove an analogue of Markov's theorem for knot isotopy in knot complements. Finally we extend this last result to prove a Markov theorem for links in an arbitrary orientable 3-manifold. (C) 1997 Elsevier Science B.V.

引用

页码：95 / 122

页数：28