Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Borsuk conjecture concerning homotopy domination   In the seminal monograph "Theory of retracts", Borsuk raised the following
question: suppose two compact ANR's are $h$--equal, i.e. mutually homotopy
dominate each other, are they homotopy equivalent? The current paper approaches
this question in two ways. On one end, we provide conditions on the fundamental
group which guarantee a positive answer to the Borsuk question. On the other
end, we construct various examples of compact $h$--equal, not homotopy
equivalent continua, with distinct properties. The first class of these
examples has trivial all known algebraic invariants (such as homology, homotopy
groups etc.) The second class is given by $n$--connected continua, for any $n$,
which are infinite $CW$--complexes, and hence ANR's, on a complement of a
point.

28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics