Rational obstruction theory and rational homotopy sets
| dc.creator | Arkowitz, M. | |
| dc.creator | Lupton, G. | |
| dc.date | 2000-10-12 | |
| dc.date.accessioned | 2026-07-07T04:37:59Z | |
| dc.date.available | 2026-07-07T04:37:59Z | |
| dc.description | We develop an obstruction theory for homotopy of homomorphisms f,g : M -> N between minimal differential graded algebras. We assume that M = Lambda V has an obstruction decomposition given by V = V_0 oplus V_1 and that f and g are homotopic on Lambda V_0. An obstruction is then obtained as a vector space homomorphism V_1 -> H^*(N). We investigate the relationship between the condition that f and g are homotopic and the condition that the obstruction is zero. The obstruction theory is then applied to study the set of homotopy classes [M, N]. This enables us to give a fairly complete answer to a conjecture of Copeland-Shar on the size of the homotopy set [A,B] when A and B are rational spaces. In addition, we give examples of minimal algebras (and hence of rational spaces) that have few homotopy classes of self-maps. | |
| dc.description | To appear, Math. Zeit | |
| dc.identifier | https://arxiv.org/abs/math/0010126 | |
| dc.identifier | http://arxiv.org/abs/math/0010126 | |
| dc.identifier | Math. Zeit., Vol. 235 (2000), 525--539. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/60114 | |
| dc.subject | Algebraic Topology | |
| dc.subject | 55P62, 55Q05, 55S35 (Primary); 55P10 (Secondary) | |
| dc.title | Rational obstruction theory and rational homotopy sets | |
| dc.type | text |