Contents
1 Introduction 1
2 List of relations 10
2.1 5-machines 10
2.2 An auxiliary group 11
2.3 The hardware of § 11
2.4 Notation 13
2.5 The rules of the ^-machine S 14
2.6 The ^-machines S and S U § 17
2.7 Converting S into a set of relations 20
2.8 Converting § into a set of relations 22
2.9 The presentation of the group *K 22
3 Th e first properties of Ji 22
3.1 Diagrams 22
3.2 S embeds into VL 23
3.3 Bands and annuli 27
3.4 Forbidden annuli 32
3.5 Surgeries involving S-cells 34
3.6 Shifting indexes 35
4 Th e group 3i2 37
5 Th e word problem in Jii 42
6 Som e special diagrams 48
6.1 #-bands and trapezia 48
6.2 Trapezia with 2-letter bases 52
6.3 Trapezia simulate the work of ^-machines 53
7 Computation s of S U S 60
7.1 Brief history 62
7.2 Standard computations 64
7.3 Tame and wild computations 73
7.4 Computations of § 78
7.5 All ring computations 83
8 Spirals 86
9 Rolls 97
9.1 Rolls without a base 98
9.2 Rolls with L-annuli 101
9.3 Rolls with base L~\K3L3 109
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