Cohomology and Hodge theory on symplectic manifolds: III
Journal
Journal of Differential Geometry
Journal Volume
103
Journal Issue
1
Pages
83-143
Date Issued
2014-02-03
Date
2014-02-03
Author(s)
Abstract
We introduce filtered cohomologies of differential forms on symplectic manifolds. They generalize and include the cohomologies discussed in Papers I and II as a subset. The filtered cohomologies are finite-dimensional and can be associated with differential elliptic complexes. Algebraically, we show that the filtered cohomologies give a two-sided resolution of Lefschetz maps, and thereby, they are directly related to the kernels and cokernels of the Lefschetz maps. We also introduce a novel, non-associative product operation on differential forms for symplectic manifolds. This product generates an A∞-algebra structure on forms that underlies the filtered cohomologies and gives them a ring structure. As an application, we demonstrate how the ring structure of the filtered cohomologies can distinguish different symplectic four-manifolds in the context of a circle times a fibered three-manifold.
Type
journal article
File(s)![Thumbnail Image]()
Loading...
Name
Hodge_spIII.pdf
Size
584.78 KB
Format
Adobe PDF
Checksum
(MD5):e26acc6ae35ea9d9e66c50331b8e0617