Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Polyfold Regularization of Constrained Moduli Spaces   We introduce tame sc-Fredholm sections and slices of sc-Fredholm sections. A
slice is a notion of subpolyfold that is compatible with the sc-Fredholm
section and has finite locally constant codimension. We prove that the subspace
of a tame polyfold that satisfies a transverse sc-smooth constraint in a finite
dimensional smooth manifold is a slice of any tame sc-Fredholm section
compatible with the constraint. Moreover, we prove that a sc-Fredholm section
restricted to a slice is a tame sc-Fredholm section with a drop in Fredholm
index given by the codimension of the slice. As a corollary, we obtain fiber
products of tame sc-Fredholm sections. We describe applications to
Gromov-Witten invariants, constructing the Piunikhin-Salamon-Schwarz maps for
general closed symplectic manifolds, and avoiding sphere bubbles in moduli
spaces of expected dimension $0$ and $1$.

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The categories of this paper are: hep-ex
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The categories of this paper are: q-bio
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The categories of this paper are: stat
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The categories of this paper are: nucl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: nlin
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: econ
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The categories of this paper are: supr-con
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: ao-sci