• Invariants and pictures[electronic resource] :low-dimensional topology and combinatorial group theory /
  • 紀錄類型: 書目-電子資源 : Monograph/item
    杜威分類號: 514/.22
    書名/作者: Invariants and pictures : low-dimensional topology and combinatorial group theory // Vassily Olegovich Manturov ... [et al.]
    其他作者: Manturov, V. O.
    出版者: Hackensack, NJ : : World Scientific,, c2020.
    面頁冊數: 1 online resource (xxiv, 357 p.) : : ill.
    標題: Low-dimensional topology.
    標題: Combinatorial group theory.
    標題: Invariants.
    ISBN: 9789811220128
    ISBN: 9811220123
    ISBN: 9789811220135
    ISBN: 9811220131
    書目註: Includes bibliographical references and index.
    內容註: Groups. Small cancellations. Greendlinger theorem -- Braid theory -- Curves on surfaces. Knots and virtual knots -- Two-dimensional knots and links -- Parity in knot theories. The parity bracket -- Cobordisms -- General theory of invariants of dynamical systems -- Groups Gk/n and their homomorphisms -- Generalisations of the groups Gk/n -- Representations of the groups Gk/n -- Realisation of spaces with Gk/n action -- Word and conjugacy problems in Gk/k+1 groups -- The groups Gk/n and invariants of manifolds -- The two-dimensional case -- The three-dimensional case -- Open problems.
    摘要、提要註: "This book contains an in-depth overview of the current state of the recently emerged and rapidly growing theory of Gk/n 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 Gk/n 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 Gk/n. The book is devoted to various realisations and generalisations of this principle in the broad sense. The groups Gk/n 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 - \Gamma_n^k, which give rise to braids on arbitrary manifolds yielding invariants of arbitrary manifolds"--
    電子資源: https://www.worldscientific.com/worldscibooks/10.1142/11821#t=toc
Export
取書館別
 
 
變更密碼
登入