Modification rule of monodromies in an R2–move

Hayano, Kenta¹

¹Department of Mathematics, Graduate School of Science, Hokkaido University, Kita 10, Nishi 8, Kita-ku, Sapporo, Hokkaido 060-0810, Japan

Algebraic and Geometric Topology, Tome 14 (2014) no. 4, pp. 2181-2222

Résumé

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.

Détail

DOI : 10.2140/agt.2014.14.2181

Classification : 57R45, 30F99
Keywords: wrinkled fibrations, homotopies of stable mappings, surface diagrams of $4$–manifolds

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