Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Topological complexity of motion planning in projective product spaces   We study Farber's topological complexity (TC) of Davis' projective product
spaces (PPS's). We show that, in many non-trivial instances, the TC of PPS's
coming from at least two sphere factors is (much) lower than the dimension of
the manifold. This is in high contrast with the known situation for (usual)
real projective spaces for which, in fact, the Euclidean immersion dimension
and TC are two facets of the same problem. Low TC-values have been observed for
infinite families of non-simply connected spaces only for H-spaces, for finite
complexes whose fundamental group has cohomological dimension not exceeding 2,
and now in this work for infinite families of PPS's. We discuss general bounds
for the TC (and the Lusternik-Schnirelmann category) of PPS's, and compute
these invariants for specific families of such manifolds. Some of our methods
involve the use of an equivariant version of TC. We also give a
characterization of the Euclidean immersion dimension of PPS's through
generalized concepts of axial maps and, alternatively, non-singular maps. This
gives an explicit explanation of the known relationship between the generalized
vector field problem and the Euclidean immersion problem for PPS's.

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The categories of this paper are: bayes-an
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
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The categories of this paper are: supr-con
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The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: comp-gas
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The categories of this paper are: atom-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-th
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: eess