{"paper":{"title":"Lagrangian cobordism functor in microlocal sheaf theory II","arxiv_id":"2308.05089","primary_cat":"math.SG","submitted_at":"2023-08-09T17:32:05+00:00","version_compiled":"v2"},"notice":"Every quoted sentence is the authors' text from the arXiv listing abstract. Labels and probabilities are the outputs of classifier-1.13.0 on the question bank abstract-p1-20260923, exactly as returned. 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Lagrangians.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.95,"main_claim_p":0.84,"quantitative":false,"quantitative_p":0.12,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.91,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.09,"interpretation":0.0}},{"i":1,"p":1.0,"id":"s1","own":true,"role":"interpretation","text":"Thus we interpret the Lagrangian cobordism functor between $Sh_{\\Lambda_\\pm}(M \\times \\mathbb{R})$ as a correspondence parametrized by $Loc({L})$.","hedge":{"p":0.96,"label":"asserted"},"own_p":0.86,"main_claim_p":0.27,"quantitative":false,"quantitative_p":0.05,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":1.0}},{"i":2,"p":0.67,"id":"s2","own":false,"role":"interpretation","text":"This enables one to consider generalizations to immersed Lagrangian cobordisms.","hedge":{"p":0.8,"label":"hedged_possibility"},"own_p":0.31,"main_claim_p":0.04,"quantitative":false,"quantitative_p":0.03,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.02,"background":0.0,"limitation":0.0,"future_work":0.3,"contribution":0.01,"interpretation":0.67}},{"i":3,"p":0.98,"id":"s3","own":true,"role":"result","text":"We also prove that the Lagrangian cobordism functor is action decreasing and recover results on the lengths of embedded Lagrangian cobordisms.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.95,"main_claim_p":0.08,"quantitative":true,"quantitative_p":0.73,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.98,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.02,"interpretation":0.0}},{"i":4,"p":0.92,"id":"s4","own":true,"role":"result","text":"Finally, using the construction of Courte-Ekholm, we obtain a family of Legendrians with sheaf categories Morita equivalent to chains of based loop spaces of the Lagrangian 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