Obstruction theory and minimal number of coincidences for maps from a complex into a manifold

Lucilía D. Borsari, Daciberg L. Gonçalves

DOI: http://dx.doi.org/10.12775/TMNA.2003.007

Abstract


The Nielsen coincidence theory is well understood for a pair of
maps between $n$-dimensional compact manifolds for $n$ greater than or equal
to three.
We consider coincidence theory of a pair $(f,g)\colon K \to \mathbb N^n$,
where $K$ is a finite simplicial complex of the same dimension as the
manifold $\mathabb N^n$.
We construct an algorithm to find the minimal number of coincidences in the
homotopy class of the pair based on the obstruction to deform the pair to
coincidence free. Some particular cases are analyzed including the one
where the target is simply connected.

Keywords


Coincidence Nielsen numbers; index; obstruction; simplicial complexes

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