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

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.

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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