Lefschetz coincidence class for several maps



The aim of this paper is to define a Lefschetz coincidence class for several maps. More specifically, for maps \({f_{1}, \ldots , f_{k} : X \rightarrow N}\) from a topological space X into a connected closed n-manifold (even nonorientable) N, a cohomological class
$$L(f_{1}, \ldots , f_{k}) \in H^{n(k-1)}(X; (f_{1}, \ldots , f_{k}) ^{\ast} (R \times \Gamma^{\ast}_{N} \times \ldots \times \Gamma^{\ast} _{N}))$$
is defined in such a way that \({L(f_{1}, \ldots , f_{k}) \neq 0}\) implies that the set of coincidences
$${\rm Coin}(f_{1}, \ldots , f_{k}) = \{x \in X\,|\,f_{1}(x) = \ldots = f_{k}(x)\}$$
is nonempty.

Mathematics Subject Classification

Primary 55M20 Secondary 54H25 


Coincidence point Lefschetz coincidence number 


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Copyright information

© Springer Basel 2015

Authors and Affiliations

  1. 1.Department of MathematicsIGCE, UNESP – Universidade Estadual PaulistaRio Claro/SPBrazil
  2. 2.Institute of MathematicsPolish Academy of SciencesWarsawPoland

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