{"paper_id":"25c667b9-a2dd-4ed9-81ed-05984d74d02e","body_text":"On Symplectically Harmonic Betti Numbers | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article On Symplectically Harmonic Betti Numbers Shanborlang Bynnud, Angom Tiken Singh This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4293971/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Brylinski introduced the symplectic analogue of harmonic forms on symplectic manifolds, thereby defining the symplectically harmonic cohomology space of a symplectic manifold. In this paper, we derive a formula for determining the sym-plectically harmonic Betti numbers of an arbitrary symplectic manifold of finite type, based on the dimensions of the kernels of the Lefschetz homomorphisms. Utilizing this formula, we compute the symplectically harmonic Betti numbers of a specific class of 4-dimensional symplectic manifolds, namely, McMullen-Taubes symplectic 4-manifolds, which includes the Kodaira-Thurston symplectic nilmanifold as a special case. MSC Classification: 53D05 , 53D35 , 57R17 , 57K43 Symplectic manifolds Symplectically harmonic Betti numbers Lefschetz map Full Text Additional Declarations No competing interests reported. Supplementary Files OnSymplecticallyharmonicBettinumbers.tex snjnl.cls Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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