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The parity of the Maslov index and the even cobordism category

Patrick M. GilmerKhaled Qazaqzeh — 2005

Fundamenta Mathematicae

We give a formula for the parity of the Maslov index of a triple of Lagrangian subspaces of a skew symmetric bilinear form over ℝ. We define an index two subcategory (the even subcategory) of a 3-dimensional cobordism category. The objects of the category are surfaces equipped with Lagrangian subspaces of their real first homology. This generalizes a result of the first author where surfaces are equipped with Lagrangian subspaces of their rational first homology.

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