A^1-homotopy groups, excision, and solvable quotients
| dc.creator | Asok, Aravind | |
| dc.creator | Doran, Brent | |
| dc.date | 2009-02-10 | |
| dc.date | 2009-03-09 | |
| dc.date.accessioned | 2026-07-07T12:49:48Z | |
| dc.date.available | 2026-07-07T12:49:48Z | |
| dc.description | We study some properties of A^1-homotopy groups: geometric interpretations of connectivity, excision results, and a re-interpretation of quotients by free actions of connected solvable groups in terms of covering spaces in the sense of A^1-homotopy theory. These concepts and results are well-suited to the study of certain quotients via geometric invariant theory. As a case study in the geometry of solvable group quotients, we investigate A^1-homotopy groups of smooth toric varieties. We give simple combinatorial conditions (in terms of fans) guaranteeing vanishing of low degree A^1-homotopy groups of smooth (proper) toric varieties. Finally, in certain cases, we can actually compute the "next" non-vanishing A^1-homotopy group (beyond π_1^{A^1}) of a smooth toric variety. From this point of view, A^1-homotopy theory, even with its exquisite sensitivity to algebro-geometric structure, is almost "as tractable" (in low degrees) as ordinary homotopy for large classes of interesting varieties. | |
| dc.description | 48 pages, To appear Adv. Math, typographical and grammatical updates | |
| dc.identifier | https://arxiv.org/abs/0902.1564 | |
| dc.identifier | http://arxiv.org/abs/0902.1564 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/222498 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Algebraic Topology | |
| dc.subject | K-Theory and Homology | |
| dc.subject | 14F35; 14M25 | |
| dc.title | A^1-homotopy groups, excision, and solvable quotients | |
| dc.type | text |