Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The anti-diagonal filtration: reduced theory and applications   Given a knot K in S^3, Seidel and Smith described in arXiv:1002.2648v3 a
graded cohomology group Kh_{symp,inv}(K), a variant of their symplectic
Khovanov cohomology group. They also constructed a spectral sequence converging
to the Heegaard Floer-hat homology group for the connected sum of the double
branched cover and a copy of S^{2}xS^{1} (with E^1-page isomorphic to a direct
summand of Kh_{symp,inv}(K)). In a previous paper (arXiv:1004.2476v5), we
showed that the higher pages of this spectral sequence are knot invariants.
Here we discuss a reduced version of the spectral sequence which directly
computes HF-hat of the double branched cover. Under some degeneration
conditions, one obtains a new absolute Maslov grading on that group. This
occurs when K is a two-bridge knot, and we compute the grading in this case. We
also extract some rational-valued knot invariants from this construction.

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The categories of this paper are: hep-th
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The categories of this paper are: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: math-ph
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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex
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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: astro-ph
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The categories of this paper are: q-fin
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The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: physics
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The categories of this paper are: cond-mat