The parity of the Maslov index and the even cobordism category

Patrick M. Gilmer; Khaled Qazaqzeh

doi:10.4064/fm188-0-5

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The parity of the Maslov index and the even cobordism category

Patrick M. Gilmer·Khaled Qazaqzeh

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Abstract

We give a formula for the parity of the Maslov index of a triple of Lagrangian subspaces of a skew symmetric bilinear form over the real numbers. We define an index two subcategory (the even subcategory) of a 3-dimensional cobordism category. The objects of the category are surfaces are 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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Patrick M. Gilmer, Khaled Qazaqzeh. 2004-01-14. The parity of the Maslov index and the even cobordism category. https://doi.org/10.4064/fm188-0-5

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