Volume 14, issue 4 (2014)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 23
Issue 2, 509–962
Issue 1, 1–508

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
Other MSP Journals
Modification rule of monodromies in an $R_2$–move

Kenta Hayano

Algebraic & Geometric Topology 14 (2014) 2181–2222
[an error occurred while processing this directive]

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.

wrinkled fibrations, homotopies of stable mappings, surface diagrams of $4$–manifolds
Mathematical Subject Classification 2010
Primary: 57R45
Secondary: 30F99
Received: 16 May 2013
Accepted: 17 December 2013
Published: 28 August 2014
Kenta Hayano
Department of Mathematics
Graduate School of Science
Hokkaido University
Kita 10
Nishi 8, Kita-ku
Sapporo, Hokkaido 060-0810