Maslov indexIn this section, we define the Maslov index and prove its properties following an unpublished text of M. Kashiwara.doi:10.1007/978-1-4684-9154-8_6Gérard LionUniversité de ParisMichèle VergneMassachusetts Institute of TechnologyBirkhäuser Boston...
^Cappell, S.E., Lee, R. and Miller, E.Y., 1994. On the Maslov index. Communications on Pure and Applied Mathematics, 47(2), pp.121-186. ^Hu, X. and Sun, S., 2009. Index and stability of symmetric periodic orbits in Hamiltonian systems with application to figure-eight orbit. Com...
准备把龙以明院士发展的Maslov指标(辛道路的指标理论)这一套方法的主要结果和框架总结一下,这是第一部分,预计会写比较多内容。这套理论总体上来看有种螺狮壳里做道场的感觉。我会比较注重我自己对一些理论的理解,方便相关方向的学生入门,当然由于是我自己写的,难免有些错漏,还请指出并且谅解。编辑...
(2018). The Maslov Index. In: The Restricted Three-Body Problem and Holomorphic Curves. Pathways in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-72278-8_10 Download citation .RIS .ENW .BIB DOIhttps://doi.org/10.1007/978-3-319-72278-8_10 Published30 August 2018 ...
Abstract. Given a mapping class f of an oriented surface and a lagrangian λ in the first homology of , we define an integer . We use to describe a universal central extension of the mapping class group of as an index-four subgroup of the extension const
We revisit the definition of the Maslov index of loops in coisotropic submanifolds tangent to the characteristic foliation of this submanifold. This Maslov index is given by the mean index of a certain symplectic path which is a lift of the holonomy along the loop. We prove a result on the...
In this paper we show that over any field of characteristic different from 2, the Maslov index gives rise to a 2-cocycle on the stable symplectic group with values in the Witt group. We also show that this cocycle admits a natural reduction to () and that the induced natural homomorphism...
Kashiwara defined the Maslov index (associated to a collection of Lagrangian subspaces of a symplectic vector space over a field F) as a class in the Witt group W(F) of quadratic forms. We construct a canonical quadratic vector space in this class and show how to understand the basic proper...
In this paper we give four definitions of Maslov index and show that they all satisfy the same system of axioms and hence are equivalent to each other. Moreover, relationships of several symplectic and differential geometric, analytic, and topological invariants (including triple Maslov indices, eta...
\\(\\eta\\)K-theoryfor\\(C^*\\)Invariants for Lagrangians of symplectic vector spaces, such as the Maslov index for paths and the Maslov triple index, have many applications in symplectic geometry and index theory. Here we study the properties of their generalizations for modules over \\...