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Coincidence free pairs of maps

Ulrich Koschorke (2006)

Archivum Mathematicum

This paper centers around two basic problems of topological coincidence theory. First, try to measure (with the help of Nielsen and minimum numbers) how far a given pair of maps is from being loose, i.e. from being homotopic to a pair of coincidence free maps. Secondly, describe the set of loose pairs of homotopy classes. We give a brief (and necessarily very incomplete) survey of some old and new advances concerning the first problem. Then we attack the second problem mainly in the setting of homotopy...

Coincidence points and maximal elements of multifunctions on convex spaces

Sehie Park (1995)

Commentationes Mathematicae Universitatis Carolinae

Generalized and unified versions of coincidence or maximal element theorems of Fan, Yannelis and Prabhakar, Ha, Sessa, Tarafdar, Rim and Kim, Mehta and Sessa, Kim and Tan are obtained. Our arguments are based on our recent works on a broad class of multifunctions containing composites of acyclic maps defined on convex subsets of Hausdorff topological vector spaces.

Computing Reidemeister classes

Davide Ferrario (1998)

Fundamenta Mathematicae

In order to compute the Nielsen number N(f) of a self-map f: X → X, some Reidemeister classes in the fundamental group π 1 ( X ) need to be distinguished. In this paper some algebraic results are given which allow distinguishing Reidemeister classes and hence computing the Reidemeister number of some maps. Examples of computations are presented.

Conjugation spaces.

Hausmann, Jean-Claude, Holm, Tara, Puppe, Volker (2005)

Algebraic & Geometric Topology

Connected covers and Neisendorfer's localization theorem

C. McGibbon, J. Møller (1997)

Fundamenta Mathematicae

Our point of departure is J. Neisendorfer's localization theorem which reveals a subtle connection between some simply connected finite complexes and their connected covers. We show that even though the connected covers do not forget that they came from a finite complex their homotopy-theoretic properties are drastically different from those of finite complexes. For instance, connected covers of finite complexes may have uncountable genus or nontrivial SNT sets, their Lusternik-Schnirelmann category...

Currently displaying 101 – 120 of 560