A general construction of partial Grothendieck transformations
| dc.creator | Schuermann, Joerg | |
| dc.date | 2002-09-23 | |
| dc.date | 2003-07-15 | |
| dc.date.accessioned | 2026-07-07T04:51:08Z | |
| dc.date.available | 2026-07-07T04:51:08Z | |
| dc.description | Fulton and MacPherson introduced the notion of bivariant theories and Grothendieck transformations related to Riemann-Roch-theorems. But there are many situations, where such a bivariant theory or a corresponding Grothendieck transformation is only partially known: characteristic classes of singular spaces (e.g. Stiefel-Whitney or Chern classes), cohomology operations (e.g. singular Adams Riemann-Roch and Steenrod operations for Chow groups) or equivariant theories (e.g. Lefschetz Riemann-Roch). We introduce in this paper a simpler notion of partial (weak) bivariant theories and partial Grothendieck transformations, which applies to all these examples. Our main theorem shows, that a natural transformation of covariant theories, which commutes with exterior products, automatically extends (uniquely) to such a partial Grothendieck transformation of suitable partial (weak) bivariant theories ! In the above geometric situations one has for example to consider only morphisms, whose target is a smooth manifold, or more generally, a suitable homology manifold. | |
| dc.description | 32 pages, no figures, some remarks and examples added, references updated | |
| dc.identifier | https://arxiv.org/abs/math/0209299 | |
| dc.identifier | http://arxiv.org/abs/math/0209299 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65040 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Algebraic Topology | |
| dc.subject | 14C17, 14C40, 55N35 | |
| dc.title | A general construction of partial Grothendieck transformations | |
| dc.type | text |