Spaces of algebraic and continuous maps between real algebraic varieties

Details Spaces of algebraic and continuous maps between real algebraic varieties Spaces of algebraic and continuous maps between real algebraic varieties

2008-09-29

arxiv.org/abs/0809.4893v4

Mathematics

Algebraic Topology

Scientific paper

We consider the inclusion of the space of algebraic (regular) maps between real algebraic varieties in the space of all continuous maps. For a certain class of real algebraic varieties, which include real projective spaces, it is well known that the space of real algebraic maps is a dense subset of the space of all continuous maps. Our first result shows that, for this class of varieties, the inclusion is also a homotopy equivalence. After proving this, we restrict the class of varieties to real projective spaces. In this case, the space of algebraic maps has a ` minimum degree\rq filtration by finite dimensional subspaces and it is natural to expect that the homotopy types of the terms of the filtration approximate closer and closer the homotopy type of the space of continuous mappings as the degree increases. We prove this and compute the lower bounds of this approximation for ` even\rq components of these spaces (more precisely, we prove a very similar and closely related result, and state this one as a conjecture).

Affiliated with

Also associated with

No associations

Rating

Spaces of algebraic and continuous maps between real algebraic varieties 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 Spaces of algebraic and continuous maps between real algebraic varieties, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Spaces of algebraic and continuous maps between real algebraic varieties will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-48789