Rank of the fundamental group of a component of a function space
| dc.creator | Lupton, Gregory | |
| dc.creator | Smith, Samuel Bruce | |
| dc.date | 2005-02-15 | |
| dc.date.accessioned | 2026-07-07T05:17:02Z | |
| dc.date.available | 2026-07-07T05:17:02Z | |
| dc.description | We compute the rank of the fundamental group of an arbitrary connected component of the space map(X, Y) for X and Y nilpotent CW complexes with X finite. For the general component corresponding to a homotopy class f : X --> Y, we give a formula directly computable from the Sullivan model for f. For the component of the constant map, our formula expresses the rank in terms of classical invariants of X and Y. Among other applications and calculations, we obtain the following: Let G be a compact simple Lie group with maximal torus T^n. Then the fundamental group of map(S^2, G/T^n; f) is a finite group if and only if f: S^2 --> G/T^n is essential. | |
| dc.identifier | https://arxiv.org/abs/math/0502311 | |
| dc.identifier | http://arxiv.org/abs/math/0502311 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74206 | |
| dc.subject | Algebraic Topology | |
| dc.subject | 55Q52; 55P15 | |
| dc.title | Rank of the fundamental group of a component of a function space | |
| dc.type | text |