论文标题
基本结和链接理论的用户指南
A user's guide to basic knot and link theory
论文作者
论文摘要
本文是说明性的，学生可以访问。我们定义了一个简单的结或链接（链接号码，ARF-Casson不变性和亚历山大 - 康威多项式）的不变性，其动机是出于有趣的结果的动机，其陈述可供非专家或学生访问。最简单的不变剂自然出现是为了解开结或链接链接。然后，我们为最简单的不变性介绍了某些“ skein'递归关系，这些关系允许引入更强大的不变性。我们以方便地计算不变式本身的方式说明了Vassiliev-Kontsevich定理，不仅是不变空间的尺寸。无需先决条件；我们以某种方式对主要概念进行了严格的定义。
This paper is expository and is accessible to students. We define simple invariants of knots or links (linking number, Arf-Casson invariants and Alexander-Conway polynomials) motivated by interesting results whose statements are accessible to a non-specialist or a student. The simplest invariants naturally appear in an attempt to unknot a knot or unlink a link. Then we present certain `skein' recursive relations for the simplest invariants, which allow to introduce stronger invariants. We state the Vassiliev-Kontsevich theorem in a way convenient for calculating the invariants themselves, not only the dimension of the space of the invariants. No prerequisites are required; we give rigorous definitions of the main notions in a way not obstructing intuitive understanding.
