Virtually spinning hyperbolic manifolds

Abstract

AbstractWe give a new proof of a result of Sullivan [Hyperbolic geometry and homeomorphisms, in Geometric topology (ed. J. C. Cantrell), pp. 543–555 (Academic Press, New York, 1979)] establishing that all finite volume hyperbolic n-manifolds have a finite cover admitting a spin structure. In addition, in all dimensions greater than or equal to 5, we give the first examples of finite-volume hyperbolic n-manifolds that do not admit a spin structure.