A Lefschetz-type coincidence theorem

Peter Saveliev

Fundamenta Mathematicae (1999)

  • Volume: 162, Issue: 1, page 65-89
  • ISSN: 0016-2736

Abstract

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A Lefschetz-type coincidence theorem for two maps f,g: X → Y from an arbitrary topological space to a manifold is given: I f g = λ f g , that is, the coincidence index is equal to the Lefschetz number. It follows that if λ f g ≠ 0 then there is an x ∈ X such that f(x) = g(x). In particular, the theorem contains well-known coincidence results for (i) X,Y manifolds, f boundary-preserving, and (ii) Y Euclidean, f with acyclic fibres. It also implies certain fixed point results for multivalued maps with “point-like” (acyclic) and “sphere-like” values.

How to cite

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Saveliev, Peter. "A Lefschetz-type coincidence theorem." Fundamenta Mathematicae 162.1 (1999): 65-89. <http://eudml.org/doc/212413>.

@article{Saveliev1999,
abstract = {A Lefschetz-type coincidence theorem for two maps f,g: X → Y from an arbitrary topological space to a manifold is given: $I_\{fg\} = λ _\{fg\}$, that is, the coincidence index is equal to the Lefschetz number. It follows that if $λ_\{fg\} ≠ 0$ then there is an x ∈ X such that f(x) = g(x). In particular, the theorem contains well-known coincidence results for (i) X,Y manifolds, f boundary-preserving, and (ii) Y Euclidean, f with acyclic fibres. It also implies certain fixed point results for multivalued maps with “point-like” (acyclic) and “sphere-like” values.},
author = {Saveliev, Peter},
journal = {Fundamenta Mathematicae},
keywords = {Lefschetz coincidence theory; Lefschetz number; coincidence index; fixed point; multivalued map; Vietoris mapping},
language = {eng},
number = {1},
pages = {65-89},
title = {A Lefschetz-type coincidence theorem},
url = {http://eudml.org/doc/212413},
volume = {162},
year = {1999},
}

TY - JOUR
AU - Saveliev, Peter
TI - A Lefschetz-type coincidence theorem
JO - Fundamenta Mathematicae
PY - 1999
VL - 162
IS - 1
SP - 65
EP - 89
AB - A Lefschetz-type coincidence theorem for two maps f,g: X → Y from an arbitrary topological space to a manifold is given: $I_{fg} = λ _{fg}$, that is, the coincidence index is equal to the Lefschetz number. It follows that if $λ_{fg} ≠ 0$ then there is an x ∈ X such that f(x) = g(x). In particular, the theorem contains well-known coincidence results for (i) X,Y manifolds, f boundary-preserving, and (ii) Y Euclidean, f with acyclic fibres. It also implies certain fixed point results for multivalued maps with “point-like” (acyclic) and “sphere-like” values.
LA - eng
KW - Lefschetz coincidence theory; Lefschetz number; coincidence index; fixed point; multivalued map; Vietoris mapping
UR - http://eudml.org/doc/212413
ER -

References

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