Geometric and homotopy theoretic methods in Nielsen coincidence theory

dc.creatorKoschorke, Ulrich
dc.date2006-06-01
dc.date.accessioned2026-07-07T07:14:43Z
dc.date.available2026-07-07T07:14:43Z
dc.descriptionIn classical fixed point and coincidence theory the notion of Nielsen numbers has proved to be extremely fruitful. Here we extend it to pairs (f_1, f_2) of maps between manifolds of arbitrary dimensions. This leads to estimates of the minimum numbers MCC(f_1, f_2) (and MC(f_1, f_2), resp.) of pathcomponents (and of points, resp.) in the coincidence sets of those pairs of maps which are homotopic to (f_1, f_2). Furthermore we deduce finiteness conditions for MC(f_1, f_2). As an application we compute both minimum numbers explicitly in four concrete geometric sample situations. The Nielsen decomposition of a coincidence set is induced by the decomposition of a certain path space E(f_1, f_2) into pathcomponents. Its higher dimensional topology captures further crucial geometric coincidence data. An analoguous approach can be used to define also Nielsen numbers of certain link maps.
dc.identifierhttps://arxiv.org/abs/math/0606026
dc.identifierhttp://arxiv.org/abs/math/0606026
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/112990
dc.subjectAlgebraic Topology
dc.subjectGeometric Topology
dc.subject55M20; 57R90; 55P35
dc.titleGeometric and homotopy theoretic methods in Nielsen coincidence theory
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