f-Vectors of 3-Manifolds

@article{Lutz2009fVectorsO3,
  title={f-Vectors of 3-Manifolds},
  author={Frank H. Lutz and Thom Sulanke and Ed Swartz},
  journal={Electr. J. Comb.},
  year={2009},
  volume={16}
}
In 1970, Walkup [46] completely described the set of f -vectors for the four 3manifolds S3, S2×S1, S2×S1, and RP . We improve one of Walkup’s main restricting inequalities on the set of f -vectors of 3-manifolds. As a consequence of a bound by Novik and Swartz [35], we also derive a new lower bound on the number of vertices that are needed for a combinatorial d-manifold in terms of its β1-coefficient, which partially settles a conjecture of Kühnel. Enumerative results and a search for small… CONTINUE READING
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