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Generalized Lefschetz numbers of pushout maps defined on non-connected spaces

Davide Ferrario (1999)

Banach Center Publications

Let A, X 1 and X 2 be topological spaces and let i 1 : A X 1 , i 2 : A X 2 be continuous maps. For all self-maps f A : A A , f 1 : X 1 X 1 and f 2 : X 2 X 2 such that f 1 i 1 = i 1 f A and f 2 i 2 = i 2 f A there exists a pushout map f defined on the pushout space X 1 A X 2 . In [F] we proved a formula relating the generalized Lefschetz numbers of f, f A , f 1 and f 2 . We had to assume all the spaces involved were connected because in the original definition of the generalized Lefschetz number given by Husseini in [H] the space was assumed to be connected. So, to extend the result of [F] to the not...

Gradient otopies of gradient local maps

Piotr Bartłomiejczyk, Piotr Nowak-Przygodzki (2011)

Fundamenta Mathematicae

We introduce various classes of local maps: gradient, gradient-like, proper etc. We prove Parusiński's theorem for otopy classes of gradient local maps.

Group actions on rational homology spheres

Stefano De Michelis (1991)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We study the homology of the fixed point set on a rational homology sphere under the action of a finite group.

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