Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Topological representations of matroids   There is a one-to-one correspondence between geometric lattices and the
intersection lattices of arrangements of homotopy spheres. When the
arrangements are essential and fully partitioned, Zaslavsky's enumeration of
the cells of the arrangement still holds. An application of the theory shows
that all minimal cellular resolutions of matroid Steiner ideals are bounded
subcomplexes of homotopy sphere arrangements of the given matroid. As a result
the Betti numbers of the ideal are computed and seen to be equivalent to
Stanley's formula in the special case of face ideals of independence complexes
of matroids.

7
The categories of this paper are: hep-th
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The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
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The categories of this paper are: econ
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
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The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
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The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
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The categories of this paper are: hep-ex