The tt* structure of the quantum cohomology of CP^1 from the viewpoint of differential geometry

Details The tt* structure of the quantum cohomology of CP^1 from the viewpoint of differential geometry The tt* structure of the quantum cohomology of CP^1 from the viewpoint of differential geometry

2009-05-24

arxiv.org/abs/0905.3876v2

Asian J. Math. 14(3), 2010, 417-437

Mathematics

Differential Geometry

25 pages, 2 figures. New version with minor revisions and updates, to appear in Asian J. Math

Scientific paper

The quantum cohomology of CP^1 provides a distinguished solution of the third Painleve equation. S. Cecotti and C. Vafa discovered this from a physical viewpoint. We derive it from a differential geometric viewpoint, using the theory of harmonic maps and in particular the generalized Weierstrass representation (DPW representation) for spacelike surfaces of constant mean curvature in Minkowski space. The nontrivial aspects are the characterization of the solution, and its global behaviour. From our point of view, the latter property says that the extended harmonic map remains entirely within a single Iwasawa orbit of the appropriate loop group.

Affiliated with

Also associated with

No associations

Rating

The tt* structure of the quantum cohomology of CP^1 from the viewpoint of differential geometry 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 The tt* structure of the quantum cohomology of CP^1 from the viewpoint of differential geometry, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The tt* structure of the quantum cohomology of CP^1 from the viewpoint of differential geometry will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-114913