Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Singular Patterns of Generic Maps of Surfaces with Boundary into the
  Plane   For generic maps from compact surfaces with boundary into the plane we
develop an explicit algorithm for minimizing both the number of cusps and the
number of components of the singular locus. More precisely, we minimize among
maps with fixed boundary conditions and prescribed singular pattern, by which
we mean the combinatorial information of how the 1-dimensional singular locus
meets the boundary. Each step of our algorithm modifies the given map only
locally by either creating or eliminating a pair of cusps. We show that the
number of cusps is an invariant modulo 2 and can be reduced to at most one, and
we compute the minimal number of components of the singular locus in terms of
the prescribed data. Applications include a discussion of pseudo-immersions as
well as the computation of state sums in Banagl's positive topological field
theory.

9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
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The categories of this paper are: dg-ga
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The categories of this paper are: econ
30
The categories of this paper are: q-alg