Fredholm-Lagrangian-Grassmannian and the Maslov index

JOURNAL OF GEOMETRY AND PHYSICS

卷:51

Review

Furutani, K

关键词: symplectic Hilbert space;    Lagrangian subspace;    Fredholm pair;    Maslov index;    Leray index;    Kashiwara index;    Hormander index;    Fredholm operator;    Fredholm-Lagrangian-Grassmannian;    elliptic operator;    K-group;    unitary group;   

DOI  :  10.1016/j.geomphys.2004.04.001

来源: Elsevier

【 摘 要 】

This is a review article on the topology of the space, so called, Fredholm-Lagrangian-Grassmannian and the quantity Maslov index for paths in this space based on the standard theory of functional analysis. Our standing point is to define the Maslov index for arbitrary paths in terms of the fundamental spectral property of the Fredholm operators as an intersection number with the Maslov cycle. This argument was first recognized by J. Phillips and was used to define the Spectral flow not only for loops but also for arbitrary paths of selfadjoint Fredholm operators. We make the arguments as elementary as possible. (C) 2004 Elsevier B.V. All rights reserved.

【 授权许可】

Free