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Desingularizing bm-Symplectic Structures.
- Source :
-
IMRN: International Mathematics Research Notices . May2019, Vol. 2019 Issue 10, p2981-2998. 18p. - Publication Year :
- 2019
-
Abstract
- A 2n-dimensional Poisson manifold (M ,Π) is said to be bm-symplectic if it is symplectic on the complement of a hypersurface Z and has a simple Darboux canonical form at points of Z which we will describe below. In this article, we will discuss a desingularization procedure which, for m even, converts Π into a family of symplectic forms ωε having the property that ωε is equal to the bm-symplectic form dual to Π outside an ε-neighborhood of Z and, in addition, converges to this form as ε tends to zero in a sense that will be made precise in the theorem below. We will then use this construction to show that a number of somewhat mysterious properties of bm-manifolds can be more clearly understood by viewing them as limits of analogous properties of the ωε's. We will also prove versions of these results for m odd; however, in the odd case the family ωε has to be replaced by a family of "folded" symplectic forms. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10737928
- Volume :
- 2019
- Issue :
- 10
- Database :
- Academic Search Index
- Journal :
- IMRN: International Mathematics Research Notices
- Publication Type :
- Academic Journal
- Accession number :
- 136579965
- Full Text :
- https://doi.org/10.1093/imrn/rnx126