Modification rule of monodromies in an R2–move

Hayano, Kenta

doi:10.2140/agt.2014.14.2181

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Modification rule of monodromies in an $R_2$–move

Kenta Hayano

Algebraic & Geometric Topology 14 (2014) 2181–2222

DOI: 10.2140/agt.2014.14.2181

Abstract

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An $R_{2}$ –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.

Keywords

wrinkled fibrations, homotopies of stable mappings, surface diagrams of $4$–manifolds

Mathematical Subject Classification 2010

Primary: 57R45

Secondary: 30F99

References

Publication

Received: 16 May 2013

Accepted: 17 December 2013

Published: 28 August 2014

Authors

Kenta Hayano
Department of Mathematics Graduate School of Science Hokkaido University Kita 10 Nishi 8, Kita-ku Sapporo, Hokkaido 060-0810 Japan
http://www.math.sci.hokudai.ac.jp/~k-hayano/index_en.html

Volume 14, issue 4 (2014)