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Closed hyperbolic manifolds without spin© structures
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DOI：10.1007/s10711-025-01060-z.png)
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Abstract
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In all dimensions n >= 5, we prove the existence of closed orientable hyperbolic manifolds that do not admit any spin(c )structure, and in fact we show that there are infinitely many commensurability classes of such manifolds. These manifolds all have non-vanishing third Stiefel-Whitney class w(3 )and are all arithmetic of simplest type. More generally, we show that for each k >= 1 and n >= 4k + 1, there exist infinitely many commensurability classes of closed orientable hyperbolic n-manifolds M with w(4k-1 )(M) not equal 0.
Keywords:
Hyperbolic manifolds
spin(c )structures
Geodesic embedding
Arithmetic manifolds
Coxeter polytopes
Coloring method
Journal
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0.5
Papers:
45
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0