Nielsen coincidence theory in arbitrary codimensions
| dc.creator | Koschorke, Ulrich | |
| dc.date | 2004-08-03 | |
| dc.date.accessioned | 2026-07-07T05:10:59Z | |
| dc.date.available | 2026-07-07T05:10:59Z | |
| dc.description | Given two maps f_1, f_2 : M^m \longrightarrow N^n between manifolds of the indicated arbitrary dimensions, when can they be deformed away from one another? More generally: what is the minimum number MCC (f_1, f_2) of pathcomponents of the coincidence space of maps f'_1, f'_2 where f'_i is homotopic to f_i, i = 1, 2? Approaching this question via normal bordism theory we define a lower bound N (f_1, f_2) which generalizes the Nielsen number studied in classical fixed point and coincidence theory (where m = n). In at least three settings N (f_1, f_2) turns out to coincide with MCC (f_1, f_2): (i) when m < 2n - 2; (ii) when N is the unit circle; and (iii) when M and N are spheres and a certain injectivity condition involving James-Hopf invariants is satisfied. We also exhibit situations where N (f_1, f_2) vanishes, but MCC (f_1, f_2) is strictly positive. | |
| dc.description | 23 pages | |
| dc.identifier | https://arxiv.org/abs/math/0408044 | |
| dc.identifier | http://arxiv.org/abs/math/0408044 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72099 | |
| dc.subject | Algebraic Topology | |
| dc.subject | Geometric Topology | |
| dc.subject | 55M20; 55M55; 55S35 (Primary) 55P35; 55Q25; 55Q55; 55Q40; 55Q57; 55R42 | |
| dc.title | Nielsen coincidence theory in arbitrary codimensions | |
| dc.type | text |