Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Traceless Character Varieties, the Link Surgeries Spectral Sequence, and
  Khovanov Homology   In arXiv:1611.09927, we constructed a well-defined Lagrangian Floer invariant
for any closed, oriented $3$-manifold $Y$ via the symplectic geometry of
so-called traceless $\mathrm{SU}(2)$-character varieties. This invariant,
$\mathrm{SI}(Y)$, which we refer to as the symplectic instanton homology of
$Y$, was also shown to satisfy an exact triangle for Dehn surgeries on knots
which is typical of Floer-theoretic invariants of $3$-manifolds.
  In this article, we demonstrate further structural properties of this
symplectic instanton homology. For example, Floer theories are expected to
roughly satisfy the axioms of a topological quantum field theory (TQFT), so
that in particular they should be functorial with respect to cobordisms.
Following a strategy used by Ozsv\'ath and Szab\'o in the context of Heegaard
Floer homology, we prove that our theory is functorial with respect to
connected $4$-dimensional cobordisms, so that cobordisms induce homomorphisms
between symplectic instanton homologies. We also generalize the surgery exact
triangle by proving that Dehn surgeries on a link $L$ in a $3$-manifold $Y$
induce a spectral sequence of symplectic instanton homologies -- the $E^2$-page
is isomorphic to a direct sum of symplectic instanton homologies of all
possible combinations of $0$- and $1$-surgeries on the components of $L$, and
the spectral sequence converges to $\mathrm{SI}(Y)$. For the branched double
cover $\Sigma(L)$ of a link $L \subset S^3$, we show there is a link surgery
spectral sequence whose $E^2$-page is isomorphic to the reduced Khovanov
homology of $L$ and which converges to the symplectic instanton homology of
$\Sigma(L)$.

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The categories of this paper are: chao-dyn
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The categories of this paper are: ao-sci
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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an
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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: acc-phys
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The categories of this paper are: plasm-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-lat
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The categories of this paper are: econ
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The categories of this paper are: solv-int