Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-orientable surfaces in homology cobordisms   We investigate constraints on embeddings of a non-orientable surface in a
$4$-manifold with the homology of $M \times I$, where $M$ is a rational
homology $3$-sphere. The constraints take the form of inequalities involving
the genus and normal Euler class of the surface, and either the
Ozsv\'ath--Sazb\'o $d$-invariants or Atiyah--Singer $\rho$-invariants of $M$.
One consequence is that the minimal genus of a smoothly embedded surface in
$L(2p,q) \times I$ is the same as the minimal genus of a surface in $L(2p,q)$.
We also consider embeddings of non-orientable surfaces in closed $4$-manifolds.

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The categories of this paper are: bayes-an
18
The categories of this paper are: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: math-ph
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
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The categories of this paper are: chem-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ex
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The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
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The categories of this paper are: solv-int
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The categories of this paper are: acc-phys