An Infrasolvmanifold Which Does Not Bound
نویسنده
چکیده
Orientable 4-dimensional infrasolvmanifolds bound orientably. We show that every non-orientable 4-dimensional infrasolvmanifold M with β = β1(M ;Q) > 0 or with geometry Nil 4 or Sol3×E1 bounds. However there are Sol 1 -manifolds which are not boundaries. The question remains open for Nil × E-manifolds. Any possible counter-examples have severely constrained fundamental groups. We also find simple cobounding 5-manifolds for all but five of the 74 flat 4-manifolds, and investigate which flat 4-manifolds embed in Rn, for n = 5, 6 or 7.
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