Overview

This book contains an in-depth overview of the current state of the recently emerged and rapidly growing theory of Gnk groups, picture-valued invariants, and braids for arbitrary manifolds. Equivalence relations arising in low-dimensional topology and combinatorial group theory inevitably lead to the study of invariants, and good invariants should be strong and apparent. An interesting case of such invariants is picture-valued invariants, whose values are not algebraic objects, but geometrical constructions, like graphs or polyhedra.In 2015, V O Manturov defined a two-parametric family of groups Gnk and formulated the following principle: if dynamical systems describing a motion of n particles possess a nice codimension 1 property governed by exactly k particles then these dynamical systems possess topological invariants valued in Gnk.The book is devoted to various realisations and generalisations of this principle in the broad sense. The groups Gnk have many epimorphisms onto free products of cyclic groups; hence, invariants constructed from them are powerful enough and easy to compare. However, this construction does not work when we try to deal with points on a 2-surface, since there may be infinitely many geodesics passing through two points. That leads to the notion of another family of groups - ?nk, which give rise to braids on arbitrary manifolds yielding invariants of arbitrary manifolds.

Full Product Details

Author:   Vassily Olegovich Manturov (Bauman Moscow State Technical Univ, Russia & Lab Of Quantum Topology, Chelyabinsk State Univ, Russia) ,  Denis Fedoseev (Moscow State Univ, Russia) ,  Seongjeong Kim (Bauman Moscow State Technical Univ, Russia) ,  Igor Nikonov (Moscow State Univ, Russia)
Publisher:   World Scientific Publishing Co Pte Ltd
Imprint:   World Scientific Publishing Co Pte Ltd
Volume:   66
ISBN:  

9789811220111

ISBN 10:   9811220115
Pages:   388
Publication Date:   11 May 2020
Audience:   College/higher education ,  Professional and scholarly ,  Tertiary & Higher Education ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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