A general construction of partial Grothendieck transformations

Details A general construction of partial Grothendieck transformations A general construction of partial Grothendieck transformations

2002-09-23

arxiv.org/abs/math/0209299v2

Mathematics

Algebraic Geometry

32 pages, no figures, some remarks and examples added, references updated

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

A general construction of partial Grothendieck transformations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A general construction of partial Grothendieck transformations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A general construction of partial Grothendieck transformations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-577014