Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Canonical bases for the equivariant cohomology and K-theory rings of
  symplectic toric manifolds   Let $M$ be a symplectic toric manifold acted on by a torus $\mathbb{T}$. In
this work we exhibit an explicit basis for the equivariant K-theory ring
$\mathcal{K}_{\mathbb{T}}(M)$ which is canonically associated to a generic
component of the moment map. We provide a combinatorial algorithm for computing
the restrictions of the elements of this basis to the fixed point set; these,
in turn, determine the ring structure of $\mathcal{K}_{\mathbb{T}}(M)$. The
construction is based on the notion of local index at a fixed point, similar to
that introduced by Guillemin and Kogan in [GK].
  We apply the same techniques to exhibit an explicit basis for the equivariant
cohomology ring $H_{\mathbb{T}}(M; \mathbb{Z})$ which is canonically associated
to a generic component of the moment map. Moreover we prove that the elements
of this basis coincide with some well-known sets of classes: the equivariant
Poincar\'e duals to the closures of unstable manifolds, and also the canonical
classes introduced by Goldin and Tolman in [GT], which exist whenever the
moment map is index increasing.

9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
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The categories of this paper are: alg-geom