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Vassily Olegovich Manturov
Invariants And Pictures: Low-dimensional Topology And Combinatorial Group Theory
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Страница 1
Invariants and Pictures
Страница 3
Страница 4
Preface
Acknowledgments
Contents
Страница 8
Chapter 1
Groups. Small Cancellations. Greendlinger Theorem
1.1Group diagrams language
1.1.1Preliminary examples
1.1.2The notion of a diagram of a group
1.1.3The van Kampen lemma
1.1.4Unoriented diagrams
1.2Small cancellation theory
1.2.1Small cancellation conditions
1.2.2The Greendlinger theorem
1.3Algorithmic problems and the Dehn algorithm
1.4The Diamond lemma
Chapter 2
Braid Theory
2.1Definitions of the braid group
2.2The stable braid group and the pure braid group
2.3The curve algorithm for braids recognition
2.3.1Construction of the invariant
2.3.2Algebraic description of the invariant
2.4Virtual braids. Inclusion of classical braids into virtual braids
2.4.1Definitions of virtual braids
2.4.2Invariants of virtual braids
2.4.2.1
A
2
n-variable generalisation of the invariant
Chapter 3
Curves on Surfaces. Knots and Virtual Knots
3.1Basic notions of knot theory
3.2Curve reduction on surfaces
3.2.1The disc flow
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