Majorana spinors on unoriented surfaces (Q2737997)

This paper exhibits the conditions for the existence of Majorana spinors on unoriented surfaces, viz. a Majorana spinor exists if and only if the genus of the surface is an odd integer. Different real spin structures are enumerated, and a parity classification is discussed together with potentially useful applications. The existence question was previously settled by \textit{B. Grinstein} and \textit{R. Rohm} [Commun. Math. Phys. 111, 667-675 (1987; Zbl 0628.53016)] using Steenrod squares, however, the methodology of the present author seems to be more comprehensive.NEWLINENEWLINENEWLINEContents include: an introduction; unoriented surfaces and double covers; spin structures on manifolds; the connection with Clifford algebras and interpretation; the number of Majorana fermions on an unoriented surface; parity classification of the Majorana fermions; and a conclusion.