The Maslov Index in Symplectic Banach Spaces (Memoirs of the American Mathematical Society) - Softcover

Bernhelm Booss-Bavnbek (author)|Chaofeng Zhu (author)

Softcover

ISBN 10: 1470428008 ISBN 13: 9781470428006

Publisher: American Mathematical Society, 2018

Synopsis

The authors consider a curve of Fredholm pair of Lagrangian subspaces in a fixed Banach space with continuously varying weak symplectic structures. Assuming vanishing index, they obtain intrinsically a continuously varying splitting of the total Banach space into pairs of symplectic subspaces. Using such decompositions the authors define the Maslov index of the curve by symplectic reduction to the classical finite-dimensional case. The authors prove the transitivity of repeated symplectic reductions and obtain the invariance of the Maslov index under symplectic reduction while recovering all the standard properties of the Maslov index.

As an application, the authors consider curves of elliptic operators which have varying principal symbol, varying maximal domain and are not necessarily of Dirac type. For this class of operator curves, the authors derive a desuspension spectral flow formula for varying well-posed boundary conditions on manifolds with boundary and obtain the splitting formula of the spectral flow on partitioned manifolds.

About this title

About the Author

Bernhelm Booss-Bavnbek, Roskilde University, Denmark.

Chaofeng Zhu, Nankai University, Tianjin, People's Republic of China.

Edition details

• Publisher: American Mathematical Society
• Publication date: 2018
• Language: English
• ISBN 10: 1470428008
• ISBN 13: 9781470428006
• Binding: Paperback
• Number of pages: 123