Applications of Klee's Dehn-Sommerville Relations

  title={Applications of Klee's Dehn-Sommerville Relations},
  author={Isabella Novik and Ed Swartz},
  journal={Discrete & Computational Geometry},
We use Klee’s Dehn-Sommerville relations and other results on face numbers of homology manifolds without boundary to (i) prove Kalai’s conjecture providing lower bounds on the f -vectors of an even-dimensional manifold with all but the middle Betti number vanishing, (ii) verify Kühnel’s conjecture that gives an upper bound on the middle Betti number of a 2k… CONTINUE READING