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Maslov Index in Symplectic Banach Spaces

Bernhelm Booss-Bavnbek
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      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.
      Format: Paperback / softback CONTRIBUTORS: Bernhelm Booss-Bavnbek EAN: 9781470428006 COUNTRY: United States PAGES: WEIGHT: 0 g HEIGHT: 254 cm
      PUBLISHED BY: American Mathematical Society DATE PUBLISHED: 2018-03-01 CITY: GENRE: MATHEMATICS / Geometry / General, MATHEMATICS / Topology WIDTH: 178 cm SPINE:

      Book Themes:

      Geometry, Topology

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      Bernhelm Booss-Bavnbek, Roskilde University, Denmark.Chaofeng Zhu, Nankai University, Tianjin, People's Republic of China.
      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.
      Format: Paperback / softback CONTRIBUTORS: Bernhelm Booss-Bavnbek EAN: 9781470428006 COUNTRY: United States PAGES: WEIGHT: 0 g HEIGHT: 254 cm
      PUBLISHED BY: American Mathematical Society DATE PUBLISHED: 2018-03-01 CITY: GENRE: MATHEMATICS / Geometry / General, MATHEMATICS / Topology WIDTH: 178 cm SPINE:

      Book Themes:

      Geometry, Topology

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      Bernhelm Booss-Bavnbek, Roskilde University, Denmark.Chaofeng Zhu, Nankai University, Tianjin, People's Republic of China.

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