Transversal Homotopy Monoids of Complex Projective Space

Details Transversal Homotopy Monoids of Complex Projective Space Transversal Homotopy Monoids of Complex Projective Space

2011-04-07

arxiv.org/abs/1104.1325v1

Mathematics

Algebraic Topology

8 pages

Scientific paper

We will give a geometric description of the nth transversal homotopy monoid of k-dimensional complex projective space, where we stratify by lower dimensional complex projective spaces in the usual way. Transversal homotopy monoids are defined as classes of based transversal maps into Whitney stratified spaces up to equivalence through such maps. We will show the nth transversal homotopy monoid of k-dimensional complex projective space is isomorphic to isotopy classes of certain filtrations of the n-sphere. The required filtrations are by nested closed subspaces $X_0 \subset ... \subset X_k=S^n$, such that the difference between any two is a manifold and the normal bundle of $X_i$ in $X_{i+1}$ is an orientable real 2-dimensional vector bundle with Euler class represented by the Poincar\'e dual of $X_{i-1}$.

Affiliated with

Also associated with

No associations

Rating

Transversal Homotopy Monoids of Complex Projective Space 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 Transversal Homotopy Monoids of Complex Projective Space, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Transversal Homotopy Monoids of Complex Projective Space will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-717965