The cone length and category of maps: pushouts, products and fibrations
| dc.creator | Arkowitz, Martin | |
| dc.creator | Stanley, Donald | |
| dc.creator | Strom, Jeffrey | |
| dc.date | 2004-06-02 | |
| dc.date.accessioned | 2026-07-07T05:08:49Z | |
| dc.date.available | 2026-07-07T05:08:49Z | |
| dc.description | For any collection of spaces A, we investigate two non-negative integer homotopy invariants of maps: l_A(f), the A-cone length of f, and L_A(f), the A-category of f. When A is the collection of all spaces, these are the cone length and category of f, respectively, both of which have been studied previously. The following results have been obtained: (1) For a map of one homotopy pushout diagram into another, we derive an upper bound for I_A and L_A of the induced map of homotopy pushouts in terms of I_A and L_A of the other maps. This has many applications including an inequality for I_A and L_A of the maps in a mapping of one mapping cone sequence into another. (2) We establish an upper bound for I_A and L_A of the product of two maps in terms of I_A and L_A of the given maps and the A-cone length of their domains. (3) We study our invariants in a pullback square and obtain as a consequence an upper bound for the A-cone length and A-category of the total space of a fibration in terms of the A-cone length and A-category of the base and fiber. We conclude with several remarks, examples and open questions. | |
| dc.description | 32 pages | |
| dc.identifier | https://arxiv.org/abs/math/0406037 | |
| dc.identifier | http://arxiv.org/abs/math/0406037 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71413 | |
| dc.subject | Algebraic Topology | |
| dc.subject | 55M30 (primary), 55P99 (secondary), 55R05 (secondary) | |
| dc.title | The cone length and category of maps: pushouts, products and fibrations | |
| dc.type | text |