Invariants And Pictures: Low-dimensional Topology And Combinatorial Group Theory. Vassily Olegovich Manturov

Invariants And Pictures: Low-dimensional Topology And Combinatorial Group Theory

Invariants And Pictures: Low-dimensional Topology And Combinatorial Group Theory - Vassily Olegovich Manturov

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in knot theories

       6.1.1Basic definitions

       6.1.2Cobordism types

       6.2Sliceness criteria

       6.2.1Odd framed graphs

       6.2.2Iteratively odd framed graphs

       6.2.3Multicomponent links

       6.2.4Other results on free knot cobordisms

       6.3L-invariant as an obstruction to sliceness

       The Groups figure

       7.General Theory of Invariants of Dynamical Systems

       7.1Dynamical systems and their properties

       7.2Free k-braids

       7.3The main theorem

       7.4Pictures

       8.Groups figure and Their Homomorphisms

       8.1Homomorphism of pure braids into figure

       8.2Homomorphism of pure braids into figure

       8.3Homomorphism into a free group

       8.4Free groups and crossing numbers

       8.5Proof of Proposition 8.3

       9.Generalisations of the Groups figure

       9.1Indices from figure and Brunnian braids

       9.2Groups figure with parity and points

       9.2.1Connection between figure and figure

       9.2.2Connection between figure and figure

       9.3Parity figure for and invariants of pure braids

       9.4Group figure with imaginary generators

       9.4.1Homomorphisms from classical braids to figure

       9.4.2Homomorphisms from figure to figure.

       9.5The groups figure for simplicial complexes

       9.5.1

-groups for simplicial complexes

       9.5.2The word problem for G2(K)

       9.6Tangent circles

       10.Representations of the Groups

       10.1Faithful representation of Coxeter groups

       10.1.1Coxeter group and its linear representation

       10.1.2Faithful representation of Coxeter groups

       10.2Groups figure and Coxeter groups C(n, 2)

       11.Realisation of Spaces with

Action

       11.1Realisation of the groups figure.

       11.1.1Preliminary definitions

       11.1.2The realisability of figure

       11.1.3Constructing a braid from a word in figure

       11.1.4The group Hk and the algebraic lemma

       11.2Realisation of

, n ≠ k + 1

       11.2.1A simple partial case

       11.2.2General

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