Face enumeration - from spheres to manifolds

• Autores: Ed Swartz
• Localización: Journal of the European Mathematical Society, ISSN 1435-9855, Vol. 11, Nº 3, 2009, págs. 449-485
• Idioma: inglés
• DOI: 10.4171/jems/156
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• Resumen

  • We prove a number of new restrictions on the enumerative properties of homology manifolds and semi-Eulerian complexes and posets. These include a determination of the affine span of the fine h-vector of balanced semi-Eulerian complexes and the toric h-vector of semi-Eulerian posets.

    The lower bounds on simplicial homology manifolds, when combined with higher dimensional analogues of Walkup�s 3-dimensional constructions [47], allow us to give a complete characterization of the f-vectors of arbitrary simplicial triangulations of S1 × S3 , CP2, K3 surfaces, and (S2 × S2) # (S2 × S2). We also establish a principle which leads to a conjecture for homology manifolds which is almost logically equivalent to the g-conjecture for homology spheres. Lastly, we show that with sufficiently many vertices, every triangulable homology manifold without boundary of dimension three or greater can be triangulated in a 2-neighborly fashion.