Nonorientable manifolds, complex and symplectic structures, and characteristic classes
Bulletin des Sciences Mathematiques
A complex manifold or a symplectic manifold is automatically oriented. We investigate these structures in the context of non-orientable manifolds. Any smooth connected non-orientable manifold is equipped with a real line bundle of order two. Various structures which are defined only on oriented manifolds extend to non-orientable manifolds once they are twisted by this line bundle of order two. Our aim is to develop this theme.
Biswas, Indranil and Datta, Mahuya, "Nonorientable manifolds, complex and symplectic structures, and characteristic classes" (2017). Journal Articles. 2509.