2018年02月22日 |  English version
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The Maslov index in symplectic Banach spaces(两场)

报告题目:The Maslov index in symplectic Banach spaces
报 告 人:朱朝锋教授 南开大学
报告时间: 10日(周三)下午2:00-3:00
          12日(周五)下午2:00-3:00
报告地点:行健楼学术活动室665
邀 请 人:董玉君 教授
报告摘要:We consider a curve of Fredholm pairs of

Lagrangian subspaces in a fixed Banach space with continuously
varying weak symplectic structures. Assuming vanishing index, we obtain intrinsically a
continuously varying splitting of the total Banach space into pairs of symplectic subspaces. Using
such decompositions we define the Maslov index of the curve by symplectic reduction to the classical
finite-dimensional case. We 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, we consider curves of elliptic operators which have varying principal symbol,
varying not necessarily of Dirac type. For this class of operator
curves, we derive a desuspension spectral flow formula for varying well-posed boundary conditions
on manifolds with boundary and obtain the splitting of the spectral flow on partitioned manifolds.
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