Topological Methods in Nonlinear Analysis

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

Lucilía D. Borsari and Daciberg L. Gonçalves

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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 $\mathbb N^n$. 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.

Article information

Source
Topol. Methods Nonlinear Anal., Volume 21, Number 1 (2003), 115-130.

Dates
First available in Project Euclid: 30 September 2016

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1475266275

Mathematical Reviews number (MathSciNet)
MR1980139

Zentralblatt MATH identifier
1045.55001

Citation

Borsari, Lucilía D.; Gonçalves, Daciberg L. Obstruction theory and minimal number of coincidences for maps from a complex into a manifold. Topol. Methods Nonlinear Anal. 21 (2003), no. 1, 115--130. https://projecteuclid.org/euclid.tmna/1475266275


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References

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