https://scholars.lib.ntu.edu.tw/handle/123456789/31821
Title: | Cohomology and Hodge theory on symplectic manifolds: III | Authors: | CHUNG-JUN TSAI Tseng, L.-S. Yau, S.-T. |
Issue Date: | 3-Feb-2014 | Journal Volume: | 103 | Journal Issue: | 1 | Start page/Pages: | 83-143 | Source: | Journal of Differential Geometry | 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. |
URI: | http://ntur.lib.ntu.edu.tw//handle/246246/271211 https://www.scopus.com/inward/record.uri?eid=2-s2.0-84963812936&doi=10.4310%2fjdg%2f1460463564&partnerID=40&md5=0a86b9370993055c8c7e26bf6be2fd17 |
DOI: | 10.4310/jdg/1460463564 |
Appears in Collections: | 數學系 |
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Hodge_spIII.pdf | 584.78 kB | Adobe PDF | View/Open |
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