Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The characteristic 2 anisotropicity of simplicial spheres   Assume D is a simplicial sphere, and k_1 is a field. We say that D is
generically anisotropic over k_1 if, for a certain purely transcendental field
extension k of k_1, a certain Artinian reduction A of the Stanley-Reisner ring
k[D] has the following property: All nonzero homogeneous elements u of A of
degree less or equal to (dim D +1)/2 have nonzero square. We prove, using
suitable differential operators, that, if the field k_1 has characteristic 2,
then every simplicial sphere D is generically anisotropic over k_1. As an
application, we give a second proof of a recent result of Adiprasito, known as
McMullen's g-conjecture for simplicial spheres. We also prove that the
simplicial spheres of dimension 1 are generically anisotropic over any field
k_1.

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The categories of this paper are: nlin
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The categories of this paper are: hep-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
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The categories of this paper are: ao-sci
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The categories of this paper are: q-bio
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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: chem-ph
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The categories of this paper are: supr-con
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The categories of this paper are: math-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: bayes-an
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The categories of this paper are: funct-an
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The categories of this paper are: plasm-ph