Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Morse moves in flow categories   We pursue the analogy of a framed flow category with the flow data of a Morse
function. In classical Morse theory, Morse functions can sometimes be locally
altered and simplified by the Morse moves. These moves include the Whitney
trick which removes two oppositely framed flowlines between critical points of
adjacent index and handle cancellation which removes two critical points
connected by a single flowline.
  A framed flow category is a way of encoding flow data such as that which may
arise from the flowlines of a Morse function or of a Floer functional. The
Cohen-Jones-Segal construction associates a stable homotopy type to a framed
flow category whose cohomology is designed to recover the corresponding Morse
or Floer cohomology. We obtain analogues of the Whitney trick and of handle
cancellation for framed flow categories: in this new setting these are moves
that can be performed to simplify a framed flow category without changing the
associated stable homotopy type.
  These moves often enable one to compute by hand the stable homotopy type
associated to a framed flow category. We apply this in the setting of the
Lipshitz-Sarkar stable homotopy type (corresponding to Khovanov cohomology) and
the stable homotopy type of a matched diagram due to the authors (corresponding
to sl_n Khovanov-Rozansky cohomology).

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The categories of this paper are: cs
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The categories of this paper are: cmp-lg
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The categories of this paper are: alg-geom
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The categories of this paper are: dg-ga
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The categories of this paper are: gr-qc
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The categories of this paper are: solv-int
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The categories of this paper are: mtrl-th
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The categories of this paper are: chem-ph
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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: math-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: stat
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The categories of this paper are: eess
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The categories of this paper are: q-fin