Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A refinement of sutured Floer homology   We introduce a refinement of the Ozsvath-Szabo complex associated to a
balanced sutured manifold $(X,\tau)$ by Juhasz. An algebra $A_\tau$ is
associated to the boundary of a sutured manifold and a filtration of its
generators by $H^2(X,\partial X;\Z)$ is defined. For a fixed Spin^c structure
$s$ over the manifold $X'$, which is obtained from $X$ by filling out the
sutures, the Ozsvath-Szabo chain complex $CF(X,\tau,s)$ is then defined as a
chain complex with coefficients in $A_\tau$ and filtered by $\SpinC(X,\tau)$.
The filtered chain homotopy type of this chain complex is an invariant of
$(X,\tau)$ and the Spin^c class $s\in\SpinC(X')$. The construction generalizes
the construction of Juhasz. It plays the role of $CF^-(X,s)$ when $X$ is a
closed three-manifold, and the role of $CFK^-(Y,K;s)$ when the sutured manifold
is obtained from a knot $K$ inside a three-manifold $Y$. Our invariants
generalize both the knot invariants of Ozsvath-Szabo and Rasmussen and the link
invariants of Ozsvath and Szabo. We study some of the basic properties of the
corresponding Ozsvath-Szabo complex, including the exact triangles, and some
form of stabilization.

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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: quant-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ph
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The categories of this paper are: q-alg
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The categories of this paper are: supr-con
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The categories of this paper are: nlin
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The categories of this paper are: atom-ph
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The categories of this paper are: physics
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The categories of this paper are: eess
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The categories of this paper are: cond-mat
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The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas