Face enumeration - from spheres to manifolds
| dc.creator | Swartz, Ed | |
| dc.date | 2007-09-25 | |
| dc.date.accessioned | 2026-07-07T08:32:06Z | |
| dc.date.available | 2026-07-07T08:32:06Z | |
| dc.description | 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 \cite{Wal}, allow us to give a complete characterization of the $f$-vectors of arbitrary simplicial triangulations of $S^1 \times S^3, \C P^2,$ $ K3$ surfaces, and $(S^2 \times S^2) # (S^2 \times S^2).$ 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. | |
| dc.description | 44 pages, 8 figures | |
| dc.identifier | https://arxiv.org/abs/0709.3998 | |
| dc.identifier | http://arxiv.org/abs/0709.3998 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/138697 | |
| dc.subject | Combinatorics | |
| dc.subject | Geometric Topology | |
| dc.subject | 13F55; 52B05 | |
| dc.title | Face enumeration - from spheres to manifolds | |
| dc.type | text |