Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Homology of torus spaces with acyclic proper faces of the orbit space   Let $X$ be 2n-dimensional compact manifold with a locally standard action of
a compact torus. The orbit space $X/T$ is a manifold with corners. Suppose that
all proper faces of $X/T$ are acyclic. In the paper we study the homological
spectral sequence $E^*_{*,*}\Rightarrow H_*(X)$ corresponding to the filtration
of $X$ by orbit types. When the free part of the action is not twisted, we
describe the whole spectral sequence in terms of homology and combinatorial
structure of $X/T$. In this case we describe the kernel and the cokernel of the
natural map $k[X/T]/(l.s.o.p.) \to H_*(X)$, where $k[X/T]$ is a face ring of
$X/T$ and $(l.s.o.p.)$ is the ideal generated by a linear system of parameters
(this ideal appears as the image of $H^{>0}(BT)$ in equivariant cohomology.
There exists a natural double grading on $H_*(X)$, which satisfies bigraded
Poincare duality. This general theory is applied to compute homology groups of
origami toric manifolds with acyclic proper faces of the orbit space. A number
of natural generalizations is considered. These include Buchsbaum simplicial
complexes and posets. h'- and h''-numbers of simplicial posets appear as the
ranks of certain terms in the spectral sequence $E^*_{*,*}$. In particular,
using topological argument we show that Buchsbaum posets have nonnegative
h''-vectors. The proofs of this paper rely on the theory of cellular sheaves.
We associate to a torus space certain sheaves and cosheaves on the underlying
simplicial poset, and observe an interesting duality between these objects.
This duality seems to be a version of Poincare-Verdier duality between cellular
sheaves and cosheaves.

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The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
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The categories of this paper are: ao-sci
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The categories of this paper are: acc-phys
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The categories of this paper are: eess
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The categories of this paper are: hep-lat
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The categories of this paper are: chem-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ph
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The categories of this paper are: physics
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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: solv-int
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The categories of this paper are: nucl-th
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The categories of this paper are: gr-qc