Simple Type and the Boundary of Moduli Space
| dc.creator | Groisser, David | |
| dc.creator | Sadun, Lorenzo | |
| dc.date | 1997-12-22 | |
| dc.date.accessioned | 2026-07-07T03:24:38Z | |
| dc.date.available | 2026-07-07T03:24:38Z | |
| dc.description | We measure, in two distinct ways, the extent to which the boundary region of moduli space contributes to the ``simple type'' condition of Donaldson theory. Using a geometric representative of μ(pt), the boundary region of moduli space contributes 6/64 of the homology required for simple type, regardless of the topology or geometry of the underlying 4-manifold. The simple type condition thus reduces to the interior of the k+1st ASD moduli space, intersected with two representatives of (4 times) the point class, being homologous to 58 copies of the k-th moduli space. This is peculiar, since the only known embeddings of the k-th moduli space into the k+1st involve Taubes gluing, and the images of such embeddings lie entirely in the boundary region. When using de Rham representatives of mu(pt), the boundary region contributes 1/8 of what is needed for simple type, again regardless of the topology or geometry of the underlying 4-manifold. The difference between this and the geometric representative answer is surprising but not contradictory, as the contribution of a fixed region to the Donaldson invariants is geometric, not topological. | |
| dc.description | LaTeX, 67 pages, including two embedded postscript figures. If you have any difficulties processing the source, send email to sadun@math.utexas.edu | |
| dc.identifier | https://arxiv.org/abs/dg-ga/9712016 | |
| dc.identifier | http://arxiv.org/abs/dg-ga/9712016 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/33407 | |
| dc.subject | Differential Geometry | |
| dc.subject | 57R57 (Primary), 58D27, 53C07, 58G99 (Secondary) | |
| dc.title | Simple Type and the Boundary of Moduli Space | |
| dc.type | text |