Homotopy invariance of spectral invariants of topological hamiltonian flows and its Lagrangian analog

Details Homotopy invariance of spectral invariants of topological hamiltonian flows and its Lagrangian analog Homotopy invariance of spectral invariants of topological hamiltonian flows and its Lagrangian analog

2011-11-25

arxiv.org/abs/1111.5992v5

Mathematics

Symplectic Geometry

86 pages; The paper is divided into 3 parts, Floer theory (Part I), homological integration theory of Lagrangian currents (Par

Scientific paper

In this paper, we prove that on any closed rational symplectic manifold $(M,\omega)$ the spectral invariant $\rho(\lambda;a)$ of a topological Hamiltonian path is invariant under the hamiltonian homotopy for any quantum cohomology class $a \in QH^*(M)$, \emph{provided} both $\lambda$ and the homotopy are supported in $U = M \setminus B$ for a fixed closed subset $B \subset M$ with nonempty interior. Some part of the proof relies much on the homological integration theory of rectifiable Lagrangian currents and its interplay with the canonical single-valued branch of the wave front of Lagrangian submanifolds, which was previously constructed by the author using the Lagrangian Floer theory on the cotangent bundle. In this paper, we further develop its geometry in the point of view of geometric measure theory. This homotopy invariance for $a=1$ is a crucial ingredient of the author's extension of Calabi homomorphism of the disc to the group of Hamiltonian homeomorphisms (also succinctly called \emph{hameomorphisms}) supported in the interior whose details are provided in a companion of this paper. This in turn proves nonsimpleness of the area preserving homeomorphism group of $D^2$ and its high dimensional analog.

Affiliated with

Also associated with

No associations

Rating

Homotopy invariance of spectral invariants of topological hamiltonian flows and its Lagrangian analog 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 Homotopy invariance of spectral invariants of topological hamiltonian flows and its Lagrangian analog, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Homotopy invariance of spectral invariants of topological hamiltonian flows and its Lagrangian analog will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-174393