Nonexistence of cusp cross-section of one-cusped complete complex hyperbolic manifolds II

Details Nonexistence of cusp cross-section of one-cusped complete complex hyperbolic manifolds II Nonexistence of cusp cross-section of one-cusped complete complex hyperbolic manifolds II

2006-03-31

arxiv.org/abs/math/0603726v1

Mathematics

Algebraic Topology

7pages

Scientific paper

D. D. Long and A. W. Reid have shown that some compact flat 3-manifold cannot be diffeomorphic to a cusp cross-section of any complete finite volume 1-cusped real hyperbolic 4-manifold. This note concerns the complex hyperbolic case. We give a negative answer that there exists a 3-dimensional closed Heisenberg infranilmanifold which cannot be diffeomorphic to a cusp cross-section of any complete finite volume 1-cusped complex hyperbolic 2-manifold.

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