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An Introduction to Knot Theory
A selection of topics which graduate students have found to be a successful introduction to the field, employing three distinct techniques: geometric topology manoeuvres, combinatorics, and algebraicExpand
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A new polynomial invariant of knots and links
The purpose of this note is to announce a new isotopy invariant of oriented links of tamely embedded circles in 3-space. We represent links by plane projections, using the customary conventions thatExpand
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A polynomial invariant of oriented links
THE THEORY of classical knots and links of simple closed curves in the 3-dimensional sphere has, for very many years, occupied a pre-eminent position in the theory of low dimensional manifolds. ItExpand
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A Representation of Orientable Combinatorial 3-Manifolds
The following question has been posed by Bing [1]: "Which compact, connected 3-manifolds can be obtained from S3 as follows: Remove a finite collection of mutually exclusive (but perhaps knotted andExpand
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Homeomorphisms of non-orientable two-manifolds
In an earlier paper (1) the idea of a c -homeomorphism on a 2-manifold was introduced; it can be described in the following way. Let the 2-manifold M contain an annulus, A , one of the boundaryExpand
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Prime knots and tangles
A study is made of a method of proving that a classical knot or link is prime. The method consists of identifying together the boundaries of two prime tangles. Examples and ways of constructing primeExpand
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Some links with non-trivial polynomials and their crossing-numbers
One of the main applications of the Jones polynomial invariant of oriented links has been in understanding links with (reduced, connected) alternating diagrams [2], [8], [9]. The Jones polynomial forExpand
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Simplicial moves on complexes and manifolds
Here are versions of the proofs of two classic theorems of combinatorial topology. The first is the result that piecewise linearly homeomorphic simplicial complexes are related by stellar moves. ThisExpand
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Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds
This is a self-contained account of the 3-manifold invariants arising from the original Jones polynomial. These are the Witten-Reshetikhin-Turaev and the Turaev-Viro invariants. Starting from theExpand
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