The parity of the Maslov index and the even cobordism category

Details The parity of the Maslov index and the even cobordism category The parity of the Maslov index and the even cobordism category

2004-01-14

arxiv.org/abs/math/0401135v2

Mathematics

Geometric Topology

7 pages, minor changes

Scientific paper

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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