The parity of the Maslov index and the even cobordism category
Volume 188 / 2005
Fundamenta Mathematicae 188 (2005), 95-102
MSC: Primary 57R56.
DOI: 10.4064/fm188-0-5
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 $\mathbb R$. 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.
