THE LEFSCHETZ NUMBER OF AN n-VALUED MULTIMAP
نویسنده
چکیده
An n-valued multimap is a continuous multivalued function φ : X ⊸ Y such that φ(x) is an unordered subset of n points of Y for each x ∈ X. If X and Y are finite polyhedra, then φ induces a graded homomorphism of homology with rational coefficients. For φ : X ⊸ X the Lefschetz number L(φ) of φ is defined to be the Lefschetz number of the induced homomorphism. If L(φ) 6= 0, then every n-valued multimap homotopic to φ has a fixed point. If X is the circle, then the Lefschetz number of φ is related to the Nielsen number N(φ) of Schirmer as in the single-valued case, that is, N(φ) = |L(φ)|. Subject Classificaton 55M20; 55N25
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