Simple Type is Not a Boundary Phenomenon
Abstract
This is an expository article, explaining recent work by D. Groisser and myself [GS] on the extent to which the boundary region of moduli space contributes to the ``simple type'' condition of Donaldson theory. The presentation is intended to complement [GS], presenting the essential ideas rather than the analytical details. It is shown that 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 4manifold. The simple type condition thus reduces to a statement about the interior of moduli space, namely that the interior of the (k+1)st ASD moduli space, intersected with two representatives of (4 times) the point class, be 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+1)st involve Taubes patching, and the image of such an embedding lies entirely in the boundary region.
 Publication:

eprint arXiv:dgga/9712015
 Pub Date:
 December 1997
 DOI:
 10.48550/arXiv.dgga/9712015
 arXiv:
 arXiv:dgga/9712015
 Bibcode:
 1997dg.ga....12015S
 Keywords:

 Differential Geometry;
 Mathematics  Differential Geometry;
 58D27 (Primary);
 58D15;
 58G99;
 53C07;
 35J60 (Secondary)
 EPrint:
 Plain TeX, 12 pages