國立臺灣大學數學系CHUNG-JUN TSAITseng, L.-S.L.-S.TsengYau, S.-T.S.-T.Yau2017-02-232018-06-282017-02-232018-06-282014-02-03http://ntur.lib.ntu.edu.tw//handle/246246/271211https://www.scopus.com/inward/record.uri?eid=2-s2.0-84963812936&doi=10.4310%2fjdg%2f1460463564&partnerID=40&md5=0a86b9370993055c8c7e26bf6be2fd17We 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.598812 bytesapplication/pdfjournal article10.4310/jdg/14604635642-s2.0-84963812936WOS:000375522200004http://ntur.lib.ntu.edu.tw/bitstream/246246/271211/1/Hodge_spIII.pdf