Geometric and homotopy theoretic methods in Nielsen coincidence theory
| dc.creator | Koschorke, Ulrich | |
| dc.date | 2006-06-01 | |
| dc.date.accessioned | 2026-07-07T07:14:43Z | |
| dc.date.available | 2026-07-07T07:14:43Z | |
| dc.description | In 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.identifier | https://arxiv.org/abs/math/0606026 | |
| dc.identifier | http://arxiv.org/abs/math/0606026 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/112990 | |
| dc.subject | Algebraic Topology | |
| dc.subject | Geometric Topology | |
| dc.subject | 55M20; 57R90; 55P35 | |
| dc.title | Geometric and homotopy theoretic methods in Nielsen coincidence theory | |
| dc.type | text |