Curve Complexes of Nonorientable Surfaces

Surfaces and their mapping class groups are central objects in geometry and low dimensional topology. Their theory is closely related to the theory of Riemann surfaces, Teichmller theory, topology and geometry of three and four dimensional smooth manifolds, symplectic manifolds and knot theory. Mapping class groups provide powerful tools in most of these theories. There are several ways of investigating algebraic and geometric properties of mapping class groups. The complexes of curves on surfaces proved very useful in the study of mapping class groups since their introduction by Harvey in 1979. Ivanov, Korkmaz and Luo proved that any automorphism of the complex of curves of an orientable surface is induced by a homeomorphism of the surface. In this book, which is the authors' Ph. D. thesis, the author proves the analogous result for nonorientable surfaces of odd genus.