Geodesic
A Lefschetz-type coincidence theorem
Fundamenta Mathematicae, Tome 162 (1999) no. 1, pp. 65-89.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/fm-162-1-65-89
Keywords: Lefschetz coincidence theory, Lefschetz number, coincidence index, fixed point, multivalued map

Peter Saveliev 1

1 
@article{10_4064_fm_162_1_65_89,
     author = {Peter Saveliev},
     title = {A {Lefschetz-type} coincidence theorem},
     journal = {Fundamenta Mathematicae},
     pages = {65--89},
     publisher = {mathdoc},
     volume = {162},
     number = {1},
     year = {1999},
     doi = {10.4064/fm-162-1-65-89},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/fm-162-1-65-89/}
}
TY  - JOUR
AU  - Peter Saveliev
TI  - A Lefschetz-type coincidence theorem
JO  - Fundamenta Mathematicae
PY  - 1999
SP  - 65
EP  - 89
VL  - 162
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/fm-162-1-65-89/
DO  - 10.4064/fm-162-1-65-89
LA  - en
ID  - 10_4064_fm_162_1_65_89
ER  - 
%0 Journal Article
%A Peter Saveliev
%T A Lefschetz-type coincidence theorem
%J Fundamenta Mathematicae
%D 1999
%P 65-89
%V 162
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/fm-162-1-65-89/
%R 10.4064/fm-162-1-65-89
%G en
%F 10_4064_fm_162_1_65_89
Peter Saveliev. A Lefschetz-type coincidence theorem. Fundamenta Mathematicae, Tome 162 (1999) no. 1, pp. 65-89. doi : 10.4064/fm-162-1-65-89. http://geodesic.mathdoc.fr/articles/10.4064/fm-162-1-65-89/

Cité par Sources :