Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Floer theory and topology of $Diff (S^2)$   We say that a fixed point of a diffeomorphism is non-degenerate if 1 is not
an eigenvalue of the linearization at the fixed point. We use
pseudo-holomorphic curves techniques to prove the following: the inclusion map
$$i: \text{Diff} ^{1} (S ^{2} ) \to \text{Diff} (S^2)$$ vanishes on all
homotopy groups, where $\text{Diff} ^{1} (S^{2} ) \subset \text {Diff} (S^{2}
)$ denotes the space of orientation preserving diffeomorphisms of $S ^{2} $
with a prescribed non-degenerate fixed point. This complements the classical
results of Smale and Eels and Earl.

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The categories of this paper are: cond-mat
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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: solv-int
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The categories of this paper are: nucl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-ex
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The categories of this paper are: adap-org
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The categories of this paper are: bayes-an
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The categories of this paper are: q-bio
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The categories of this paper are: nlin
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The categories of this paper are: ao-sci
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The categories of this paper are: quant-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: cs