Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Morse-Bott Split Symplectic Homology   We introduce a chain complex associated to a Liouville domain $(\overline{W},
d\lambda)$ whose boundary $Y$ admits a Boothby--Wang contact form (i.e. is a
prequantization space). The differential counts cascades of Floer solutions in
the completion $W$ of $\overline{W}$, in the spirit of Morse--Bott homology (as
in work of Bourgeois, Frauenfelder arXiv:math/0309373 and Bourgeois-Oancea
arXiv:0704.1039). The homology of this complex is the symplectic homology of
the completion $W$.
  We identify a class of simple cascades and show that their moduli spaces are
cut out transversely for generic choice of auxiliary data. If $X$ is obtained
by collapsing the boundary along Reeb orbits and $\Sigma$ is the quotient of
$Y$ by the $S^1$-action induced by the Reeb flow, we also establish
transversality for certain moduli spaces of holomorphic spheres in $X$ and in
$\Sigma$.
  Finally, under monotonicity assumptions on $X$ and $\Sigma$, we show that for
generic data, the differential in our chain complex counts elements of moduli
spaces that are transverse. Furthermore, by some index estimates, we show that
very few combinatorial types of cascades can appear in the differential.

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The categories of this paper are: hep-lat
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The categories of this paper are: adap-org
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The categories of this paper are: cmp-lg
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The categories of this paper are: physics
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The categories of this paper are: chem-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: q-fin
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The categories of this paper are: cond-mat
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The categories of this paper are: mtrl-th
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The categories of this paper are: supr-con
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-th
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The categories of this paper are: solv-int
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The categories of this paper are: eess
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The categories of this paper are: bayes-an
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The categories of this paper are: chao-dyn