Rational maps and string topology

Details Rational maps and string topology Rational maps and string topology

2003-09-07

arxiv.org/abs/math/0309137v4

Geom. Topol. 10 (2006) 1579-1606

Mathematics

Algebraic Topology

This is the version published by Geometry & Topology on 28 October 2006

Scientific paper

10.2140/gt.2006.10.1579

We apply a version of the Chas-Sullivan-Cohen-Jones product on the higher loop homology of a manifold in order to compute the homology of the spaces of continuous and holomorphic maps of the Riemann sphere into a complex projective space. This product makes sense on the homology of maps from a co-H space to a manifold, and comes from a ring spectrum. We also build a holomorphic version of the product for maps of the Riemann sphere into homogeneous spaces. In the continuous case we define a related module structure on the homology of maps from a mapping cone into a manifold, and then describe a spectral sequence that can compute it. As a consequence we deduce a periodicity and dichotomy theorem when the source is a compact Riemann surface and the target is a complex projective space.

Affiliated with

Also associated with

No associations

Rating

Rational maps and string topology 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 Rational maps and string topology, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Rational maps and string topology will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-47794