欢迎光临澳大利亚新华书店网 [登录 | 免费注册]

    • 覆盖对应和非交换几何(英文)/国外优秀数学著作原版系列
      • 作者:(伊拉克)阿哈默德·扎尼·阿尔-雅西里|责编:王勇钢//李烨
      • 出版社:哈尔滨工业大学
      • ISBN:9787560399157
      • 出版日期:2022/01/01
      • 页数:119
    • 售价:11.2
  • 内容大纲

        In this thesis we construct an additive category whose objects are embedded graphs (or in particular knots) in the 3-sphere and where morphisms are formal linear combinations of 3-manifolds. Our definition of correspondences relies on the Alexander branched covering theorem [1], which shows that all compact oriented 3-manifolds can be realized as branched coverings of the 3-sphere, with branched locus an embedded (not necessarily connected) graph. The way in which a given 3-manifold is realized as a branched cover is highly not unique. It is precisely this lack of uniqueness that makes it possible to regard 3-manifolds as correspondences. In fact, we show that, by considering a 3-manifold M realized in two different ways as a covering of the 3-sphere as defining a correspondence between the branch loci of the two covering maps, we obtain a well defined associative composition of correspondences given by the fibered product.
  • 作者介绍

  • 目录

    1.Introduction
    Chapter 1.Graphs Category and Three-manifolds as correspondences
      1.Three-manifolds as correspondences
      2.Composition ofcorrespondencas
      3.Representations and compositions of correspondences
      4.Semigroupoids and additive categories
      5.Categories of graphs and correspondences
      6.Convolution algebra and time evolution
      7.Equivalence of correspondences
      8.Convolution algebras and 2-semigroupoids
      9.Vertical and horizontal time evolutions
      10.Vertical time evolution: Hattie-Hawking gravity
      11.Vertical time evolution: gauge moduli and index theory
      12.Horizontal time evolution: bivariant Chern character
      13.Noncommutative spaces and spectral correspondences
    Chapter 2.Knots, Khovanov Homology
      1.Introduction
      2.From graphs to knots
      3.Khovanov Homology
      4.Knots and Links Cobordism Groups
      5.Graphs and cobordisms
      6.Homology theories for embedded graphs
      7.Questions and Future Work
    Appendix A.
      1.Branched Covering
      2.Filtration
      3.Knot and link
      4.Topological Quantum Field Theory
      5.2-Category
      6.Group Rings
      7.Creation and annihilation operators
      8.A quick introduction to Dirac operators
      9.Concepts of Cyclic Cohomology
    Appendix.Bibliography
    编辑手记

同类热销排行榜

推荐书目

  • 孩子你慢慢来/人生三书 华人世界率性犀利的一枝笔,龙应台独家授权《孩子你慢慢来》20周年经典新版。她的《...

  • 时间简史(插图版) 相对论、黑洞、弯曲空间……这些词给我们的感觉是艰深、晦涩、难以理解而且与我们的...

  • 本质(精) 改革开放40年,恰如一部四部曲的年代大戏。技术突变、产品迭代、产业升级、资本对接...

更多>>>