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In this short note we discuss certain examples of Legendrian submanifolds, whose linearized Legendrian contact (co)homology groups over integers have non-vanishing algebraic torsion. More precisely, for a given arbitrary finitely generated abelian group and a positive integer , , we construct examples of Legendrian submanifolds of the standard contact vector space , whose -th linearized Legendrian contact (co)homology over computed with respect to a certain augmentation is isomorphic to .

生成讲解博客的中文版本

生成AI智能校验的中文版本