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

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rel="nofollow" href="#litres_trial_promo">9.2.2Connection between and

       9.3Parity for and invariants of pure braids

       9.4Group with imaginary generators

       9.4.1Homomorphisms from classical braids to

       9.4.2Homomorphisms from to .

       9.5The groups 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 and Coxeter groups C(n, 2)

       11.Realisation of Spaces with

Action

       11.1Realisation of the groups .

       11.1.1Preliminary definitions

       11.1.2The realisability of

       11.1.3Constructing a braid from a word in

       11.1.4The group Hk and the algebraic lemma

       11.2Realisation of

, n ≠ k + 1

       11.2.1A simple partial case

       11.2.2General construction

       11.3The

-complex

       12.Word and Conjugacy Problems in Groups

       12.1Conjugacy problem in

       12.1.1Existence of the algorithmic solution

       12.1.2Algorithm of solving the conjugacy problem in

       12.2The word problem for

       12.2.1Presentation of the group H₄

       12.2.2The Howie diagrams

       12.2.3The solution to the word problem in H₄

       13.The Groups

and Invariants of Manifolds

       13.1Projective duality

       13.2Embedded hypersurfaces

       13.2.1Examples

       13.3Immersed hypersurfaces

       13.4Circles in 2-manifolds and the group

       13.5Immersed curves in M²

       13.6A map from knots to 2-knots

       Manifolds of Triangulations

      

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