Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Modification rule of monodromies in R_2-move   An R_2-move is a homotopy of wrinkled fibrations which deforms images of
indefinite fold singularities like Reidemeister move of type II. Variants of
this move are contained in several important deformations of wrinkled
fibrations, flip and slip for example. 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 one reference
fiber of a fibration, which is obtained by applying flip and slip to the
original fibration, in terms of mapping class groups. As an application of this
algorithm, we give several examples of diagrams which were introduced by
Williams to describe smooth 4-manifolds by simple closed curves of closed
surfaces.

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The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an