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Acta Mathematica Sinica, English Series

, Volume 35, Issue 2, pp 239–244 | Cite as

Coincidence Wecken Property for Nilmanifolds

  • Daciberg GonçalvesEmail author
  • Peter Wong
Article
  • 14 Downloads

Abstract

Let \(f,g : X \rightarrow Y\) be maps from a compact infra-nilmanifold X to a compact nilmanifold Y with \(X \geq \rm{dim}\it{Y}\). In this note, we show that a certain Wecken type property holds, i.e., if the Nielsen number N(f, g) vanishes then f and g are deformable to be coincidence free. We also show that if X is a connected finite complex X and the Reidemeister coincidence number R(f, g) = ∞ then f ~ f′ so that \(C(f',g)= \{x \in X|f'(x)=g(x)\}\) is empty.

Keywords

Nielsen coincidence theory nilmanifolds 

MR(2010) Subject Classification

55M20 22E25 

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References

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Copyright information

© Institute of Mathematics, Academy of Mathematics and Systems Science (CAS), Chinese Mathematical Society (CAS) and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Departamento de Matemática-IME-Universidade de São PauloSão PauloBrazil
  2. 2.Department of MathematicsBates CollegeLewistonUSA

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