Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Isometric realization of cross caps as formal power series and its
  applications   Two cross caps in Euclidean $3$-space are said to be formally isometric if
their Taylor expansions of the first fundamental forms coincide by taking a
suitable local coordinate system. For a given $C^\infty$ cross cap $f$, we give
a method to find all cross caps which are formally isometric to $f$. As an
application, we give a countable family of intrinsic invariants of cross caps
which recognizes formal isometry classes completely.

6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
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The categories of this paper are: funct-an
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The categories of this paper are: math-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
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The categories of this paper are: nlin