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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm188-0-5,
author = {Patrick M. Gilmer and Khaled Qazaqzeh},
title = {The parity of the Maslov index and the even cobordism category},
journal = {Fundamenta Mathematicae},
volume = {185},
year = {2005},
pages = {95-102},
zbl = {1157.57303},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm188-0-5}
}
Patrick M. Gilmer; Khaled Qazaqzeh. The parity of the Maslov index and the even cobordism category. Fundamenta Mathematicae, Tome 185 (2005) pp. 95-102. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm188-0-5/