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

Abstract

This paper has crucial flaws in the construction of measure in the proof of Theorem 11.1 in Part II and so withdrawn. Part I is independent of Part II whose content is salient has independent interest.

This paper is withdrawn by the author due to crucial flaws in the arguments provided in Part II for the proof of Theorem 11.1. Homotopy invariance of spectral invariance (and hence the simpleness question) is still an open question. (However the materials in Part I are independent of Part II and salient.)

References in corpus (4)

• On the uniqueness of generating Hamiltonian for continuous limits of Hamiltonians flows
• Locality of continuous Hamiltonian flows and Lagrangian intersections with the conormal of open subsets
• Quasi-morphisms on cotangent bundles and symplectic homogenization
• Localization of Floer homology of engulfable topological Hamiltonian loop

Cited by in corpus (3)

• Localization of Floer homology of engulfable topological Hamiltonian loop
• Extension of Calabi homomorphism and non-simpleness of the area preserving homeomorphism group of $D^2$
• Cliff-wall surgery and vanishing of basic phase function for contractible topological Hamiltonian loop