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Virtually spinning hyperbolic manifolds

Part of: Topological manifolds

Published online by Cambridge University Press:  05 December 2019

D. D. Long  and
A. W. Reid
D. D. Long
Affiliation:
Department of Mathematics, University of California, Santa Barbara, CA93106, USA ([email protected])
A. W. Reid
Affiliation:
Department of Mathematics, Rice University, Houston, TX77005, USA ([email protected])
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Abstract

We 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.

Keywords

hyperbolic manifoldspin structure

MSC classification

Primary: 57N65: Algebraic topology of manifolds
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 63 , Issue 2 , May 2020 , pp. 305 - 313
Copyright
Copyright © Edinburgh Mathematical Society 2019

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