PreprintCC BY 4.0arXiv
Maslov Indicies In Symplectic Geometry Revisited
Abstract
Thirty years ago in ``On the Maslov Index'' the present authors with their late collaborator Prof. Ronnie Lee of Yale University presented an axiomatization of the Maslov index, an integer-valued invariant of continuous, piecewise smooth paths of pairs of Lagrangians. Four distinct methods of definition of such Maslov indicies were given; each satisfying the axioms. Here two more are offered and comparisons are made to the recent work of Her and Zhong defining an invariant of a path of symplectic matrices motivated by earlier work of Lidskii and Gelfand, Salomon and Zehnder.
Related
- The shifted symplectic geometry of derived higher groupoids
- A De Rham Perspective on the Symplectic Geometry of Teichmüller Space
- Three-Dimensional Coulomb Discrete Spectrum via Symplectic Geometry and Phase-Space Constraints: A Geometric Framework for Condensed-Matter Coulomb-Like Systems
- The Chrysene Formalism Revisited: A Twelve-Axiom Foundation for Molecular Characterization, Tensorial Noncommutative Geometry, and Operator Response
- Rigidity of Lagrangian submanifolds with conformal Maslov form and Legendrian capillary boundary
BibTeX
@misc{cappell2026maslov,
title = {{Maslov Indicies In Symplectic Geometry Revisited}},
author = {Sylvain E. Cappell and Edward Y. Miller},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.03061},
eprint = {2609.03061},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.03061},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Maslov Indicies In Symplectic Geometry Revisited
AU - Sylvain E. Cappell
AU - Edward Y. Miller
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2609.03061
UR - https://arxiv.org/abs/2609.03061
AB - Thirty years ago in ``On the Maslov Index'' the present authors with their late collaborator Prof. Ronnie Lee of Yale University presented an axiomatization of the Maslov index, an integer-valued invariant of continuous, piecewise smooth paths of pairs of Lagrangians. Four distinct methods of definition of such Maslov indicies were given; each satisfying the axioms. Here two more are offered and comparisons are made to the recent work of Her and Zhong defining an invariant of a path of symplectic matrices motivated by earlier work of Lidskii and Gelfand, Salomon and Zehnder.
ER -