Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonstabilized Nielsen coincidence invariants and Hopf--Ganea
  homomorphisms   In classical fixed point and coincidence theory the notion of Nielsen numbers
has proved to be extremely fruitful. We extend it to pairs (f_1,f_2) of maps
between manifolds of arbitrary dimensions, using nonstabilized normal bordism
theory as our main tool. This leads to estimates of the minimum numbers
MCC(f_1,f_2) (and MC(f_1,f_2), respectively) of path components (and of points,
resp.) in the coincidence sets of those pairs of maps which are homotopic to
(f_1,f_2). Furthermore, we deduce finiteness conditions for MC(f_1,f_2). As an
application we compute both minimum numbers explicitly in various concrete
geometric sample situations.
  The Nielsen decomposition of a coincidence set is induced by the
decomposition of a certain path space E(f_1,f_2) into path components. Its
higher dimensional topology captures further crucial geometric coincidence
data. In the setting of homotopy groups the resulting invariants are closely
related to certain Hopf--Ganea homomorphisms which turn out to yield finiteness
obstructions for MC.

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The categories of this paper are: bayes-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: patt-sol
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The categories of this paper are: supr-con
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The categories of this paper are: gr-qc
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The categories of this paper are: ao-sci
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-ex
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The categories of this paper are: stat
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ph
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The categories of this paper are: q-fin
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The categories of this paper are: astro-ph