HARVARD
MATH 139 -
Symplectic geometry
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Symplectic GeometryLecture 3.The linear symplectic category.The purpose of today’s lecture is to describe the category whose objects are symplectic vector spaces and whose morphisms are the linear canonical relations. Everything in these this lecture reflects joint work with Victor Guillemin.References for today:The axioms for a category:Functors and morphisms.Involutory functors.Involutive functors.The associative law.“Points” of FinRel.The twisted diagonal..The associative law via “points”.The involutive structure on FinRel.Enhancing the category FinRel.A basic example:Linear canonical relations.The kernel of .Main theorem of
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