Modification rule of monodromies in an R2-move

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5 Citations (Scopus)


An R2-move is a homotopy of wrinkled fibrations which deforms images of indefinite fold singularities like the Reidemeister move of type II. Variants of this move are contained in several important deformations of wrinkled fibrations. In this paper, we first investigate how monodromies are changed by this move. For a given fibration and its vanishing cycles, we then give an algorithm to obtain vanishing cycles in a single reference fiber of a fibration obtained by flip and slip, which is a sequence of homotopies increasing fiber genera. As an application of this algorithm, we give several examples of diagrams which were introduced by Williams to describe smooth 4-manifolds by a finite sequence of simple closed curves in a closed surface.

Original languageEnglish
Pages (from-to)2181-2222
Number of pages42
JournalAlgebraic and Geometric Topology
Issue number4
Publication statusPublished - 2014 Aug 28
Externally publishedYes


  • Homotopies of stable mappings
  • Surface diagrams of 4 –manifolds
  • Wrinkled fibrations

ASJC Scopus subject areas

  • Geometry and Topology


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