Holomorphic disc, spin structures and Floer cohomology of the Clifford torus

Details Holomorphic disc, spin structures and Floer cohomology of the Clifford torus Holomorphic disc, spin structures and Floer cohomology of the Clifford torus

2003-08-25

arxiv.org/abs/math/0308224v1

Mathematics

Symplectic Geometry

31 pages, 2 figures

Scientific paper

We compute the Bott-Morse Floer cohomology of the Clifford torus in $\CP^n$ with all possible spin-structures. Each spin structure is known to determine an orientation of the moduli space of holomorphic discs, and we analyze the change of orientation according to the change of spin structure of the Clifford torus. Also, we classify all holomorphic discs with boundary lying on the Clifford torus by establishing a Maslov index formula for such discs. As a result, we show that in odd dimensions there exist two spin structures which give non-vanishing Floer cohomology of the Clifford torus, and in even dimensions, there is only one such spin structure. When the Floer cohomology is non-vanishing, it is isomorphic to the singular cohomology of the torus (with a Novikov ring as its coefficients). As a corollary, we prove that any Hamiltonian deformation of the Clifford torus intersects with it at least at $2^n$ distinct intersection points, when the intersection is transversal. We also compute the Floer cohomology of the Clifford torus with flat line bundles on it and verify the prediction made by Hori using a mirror symmetry calculation.

Affiliated with

Also associated with

No associations

Rating

Holomorphic disc, spin structures and Floer cohomology of the Clifford torus 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 Holomorphic disc, spin structures and Floer cohomology of the Clifford torus, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Holomorphic disc, spin structures and Floer cohomology of the Clifford torus will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-629471