Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An elementary alternative to ECH capacities   The ECH capacities are a sequence of numerical invariants of symplectic
four-manifolds which give (sometimes sharp) obstructions to symplectic
embeddings. These capacities are defined using embedded contact homology, and
establishing their basic properties currently requires Seiberg-Witten theory.
In this note we define a new sequence of symplectic capacities in four
dimensions using only basic notions of holomorphic curves. The new capacities
satisfy the same basic properties as ECH capacities and agree with the ECH
capacities for the main examples for which the latter have been computed,
namely convex and concave toric domains. The new capacities are also useful for
obstructing symplectic embeddings into closed symplectic four-manifolds. This
work is inspired by a recent preprint of McDuff-Siegel giving a similar
elementary alternative to symplectic capacities from rational SFT.

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The categories of this paper are: nucl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: alg-geom
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: comp-gas
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The categories of this paper are: stat
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: physics
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The categories of this paper are: q-fin
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The categories of this paper are: ao-sci
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The categories of this paper are: bayes-an
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The categories of this paper are: q-alg
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The categories of this paper are: atom-ph