The Maslov index in weak symplectic functional analysis
Differential Geometry
2013-12-10 v1 High Energy Physics - Theory
Functional Analysis
Symplectic Geometry
Spectral Theory
Abstract
We recall the Chernoff-Marsden definition of weak symplectic structure and give a rigorous treatment of the functional analysis and geometry of weak symplectic Banach spaces. We define the Maslov index of a continuous path of Fredholm pairs of Lagrangian subspaces in continuously varying Banach spaces. We derive basic properties of this Maslov index and emphasize the new features appearing.
Keywords
Cite
@article{arxiv.1301.7248,
title = {The Maslov index in weak symplectic functional analysis},
author = {Bernhelm Booss-Bavnbek and Chaofeng Zhu},
journal= {arXiv preprint arXiv:1301.7248},
year = {2013}
}
Comments
34 pages, 13 figures, 45 references, to appear in Ann Glob Anal Geom. The final publication will be available at http://www.springerlink.com. arXiv admin note: substantial text overlap with arXiv:math/0406139