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The braid groups, knots and algebraic geometry

โœ Scribed by Joan S. Birman; Mina Teicher

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
232 KB
Volume
78
Category
Article
ISSN
0166-8641

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The Jones polynomial was originally defined by constructing a Markov trace on the sequence of Temperley-Lieb algebras. In this paper we give a programme for constructing other link invariants by the same method. The data for the constructions is a representation of the three string braid group.

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The object of this paper, which is the first in a series of three, is to lay the foundations of the theory of ideals and algebraic sets over groups. แฎŠ 1999 Aca- demic Press CONTENTS 1. Introduction. 1.1. Some general comments. 1.2. The category of G-groups. 1.3. Notions from commutative algebra. 1.4

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In this paper we show that each element ฮฑ of the pure braid group P n or the pure symmetric automorphism group H (n) of the free group F n of rank n can be represented as the special Lie algebra of Cartan type. There is a corresponding action of these groups on C[[a 1 , . . . , a r ]] and C[a 1 , .