An upper bound on Reidemeister moves

<abstract abstract-type="TeX"><p> We provide an explicit upper bound on the number of Reidemeister moves required to pass between two diagrams of the same link. This leads to a conceptually simple solution to the equivalence problem for links.

[1]  K. Reidemeister,et al.  Knoten und Gruppen , 1927 .

[2]  W. Haken.  Theorie der Normalflächen , 1961 .

[3]  W. T. Tutte.  A Census of Planar Maps , 1963, Canadian Journal of Mathematics.

[4]  Klaus Johannson,et al.  Homotopy Equivalences of 3-Manifolds with Boundaries , 1979 .

[5]  Geoffrey Hemion,et al.  On the classification of homeomorphisms of 2-manifolds and the classification of 3-manifolds , 1979 .

[6]  G. Budworth.  The Knot Book , 1983 .

[7]  M. Culler,et al.  Bounded, separating, incompressible surfaces in knot manifolds , 1984 .

[8]  J. Hass,et al.  Intersections of curves on surfaces , 1985 .

[9]  U. Pachner,et al.  Konstruktionsmethoden und das kombinatorische Homöomorphieproblem für Triangulationen kompakter semilinearer Mannigfaltigkeiten , 1987 .

[10]  Udo Pachner,et al.  P.L. Homeomorphic Manifolds are Equivalent by Elementary 5hellingst , 1991, Eur. J. Comb..

[11]  C. Adams.  Tales of Topology. (Book Reviews: The Knot Book. An Elementary Introduction to the Mathematical Theory of Knots.) , 1994 .

[12]  Abigail Thompson,et al.  THIN POSITION AND THE RECOGNITION PROBLEM FOR S3 , 1994 .

[13]  Alexander Nabutovsky,et al.  Einstein structures: Existence versus uniqueness , 1995 .

[14]  Z. Sela.  The isomorphism problem for hyperbolic groups I , 1995 .

[15]  Walter D. Neumann,et al.  Canonical decompositions of 3–manifolds , 1997, math/9712227.

[16]  Ronald C. Read,et al.  The knot book: An elementary introduction to the mathematical theory of knots , 1997, Complex..

[17]  J. Lagarias,et al.  The number of Reidemeister moves needed for unknotting , 1998, math/9807012.

[18]  W. B. R. Lickorish.  Simplicial moves on complexes and manifolds , 1999 .

[19]  Aleksandar Mijatović.  Triangulations of Seifert fibred manifolds , 2003 .

[20]  Aleksandar Mijatovic.  Simplical structures of knot complements , 2003 .

[21]  Sergei Matveev,et al.  Algorithmic Topology and Classification of 3-Manifolds , 2003 .

[22]  Aleksandar Mijatovic.  Triangulations of fibre-free Haken 3-manifolds , 2003 .

[23]  A. Mijatović.  Simplifying triangulations of S3 , 2003 .

[24]  C. Hayashi.  The number of Reidemeister moves for splitting a link , 2005 .

[25]  D. Groves,et al.  The isomorphism problem for toral relatively hyperbolic groups , 2005, math/0512605.

[26]  R. Ho.  Algebraic Topology , 2022 .