On face numbers of manifolds with symmetry |
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Authors: | Isabella Novik |
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Institution: | Department of Mathematics, University of Washington, Box 354350 (C-416 Padelford), Seattle, WA 98195-4350, USA |
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Abstract: | Necessary conditions on the face numbers of Cohen-Macaulay simplicial complexes admitting a proper action of the cyclic group of a prime order are given. This result is extended further to necessary conditions on the face numbers and the Betti numbers of Buchsbaum simplicial complexes with a proper -action. Adin's upper bounds on the face numbers of Cohen-Macaulay complexes with symmetry are shown to hold for all (d−1)-dimensional Buchsbaum complexes with symmetry on n?3d−2 vertices. A generalization of Kühnel's conjecture on the Euler characteristic of 2k-dimensional manifolds and Sparla's analog of this conjecture for centrally symmetric 2k-manifolds are verified for all 2k-manifolds on n?6k+3 vertices. Connections to the Upper Bound Theorem are discussed and its new version for centrally symmetric manifolds is established. |
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Keywords: | Cohen-Macaulay and Buchsbaum complexes Initial ideals Clements-Lindströ m theorem |
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