Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Borsuk-Ulam Theorems for Complements of Arrangements   In combinatorial problems it is sometimes possible to define a
$G$-equivariant mapping from a space $X$ of configurations of a system to a
Euclidean space $\mathbb{R}^m$ for which a coincidence of the image of this
mapping with an arrangement $\mathcal{A}$ of linear subspaces insures a desired
set of linear conditions on a configuration. Borsuk-Ulam type theorems give
conditions under which no $G$-equivariant mapping of $X$ to the complement of
the arrangement exist. In this paper, precise conditions are presented which
lead to such theorems through a spectral sequence argument. We introduce a blow
up of an arrangement whose complement has particularly nice cohomology making
such arguments possible. Examples are presented that show that these conditions
are best possible.

19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex