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arXiv · 0805.2773

Applications of Klee's Dehn-Sommerville relations

Isabella Novik·Ed Swartz
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Abstract

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-dimensional manifold in terms of k and the number of vertices, and (iii) partially prove Kühnel's conjecture providing upper bounds on other Betti numbers of odd- and even-dimensional manifolds. For manifolds with boundary, we derive an extension of Klee's Dehn-Sommerville relations and strengthen Kalai's result on the number of their edges.

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Isabella Novik, Ed Swartz. 2008-05-19. Applications of Klee's Dehn-Sommerville relations. https://arxiv.org/abs/0805.2773

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