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An Introduction to Knot Theory

- W. Lickorish
- Mathematics
- 3 October 1997

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 algebraic… Expand

576 57

A new polynomial invariant of knots and links

- P. Freyd, D. Yetter, J. Hoste, W. Lickorish, K. Millett, A. Ocneanu
- Mathematics
- 1 April 1985

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 that… Expand

998 32- PDF

A polynomial invariant of oriented links

- W. Lickorish, K. Millett
- Mathematics
- 1987

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. It… Expand

283 28- PDF

A finite set of generators for the homeotopy group of a 2-manifold

- W. Lickorish
- Mathematics
- 1 October 1964

285 23

A Representation of Orientable Combinatorial 3-Manifolds

- W. Lickorish
- Mathematics
- 1 November 1962

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 and… Expand

466 21- PDF

Homeomorphisms of non-orientable two-manifolds

- W. Lickorish
- Mathematics
- 1 April 1963

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 boundary… Expand

137 17

Prime knots and tangles

- W. Lickorish
- Mathematics
- 1981

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 prime… Expand

94 16- PDF

Some links with non-trivial polynomials and their crossing-numbers

- W. Lickorish, M. Thistlethwaite
- Mathematics
- 1 December 1988

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 for… Expand

156 16

Simplicial moves on complexes and manifolds

- W. Lickorish
- Mathematics
- 20 November 1999

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. This… Expand

147 10- PDF

Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds

- W. Lickorish
- Mathematics
- 5 July 1994

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 the… Expand

66 8

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