f-Vectors of 3-Manifolds
| dc.creator | Lutz, Frank H. | |
| dc.creator | Sulanke, Thom | |
| dc.creator | Swartz, Ed | |
| dc.date | 2008-05-08 | |
| dc.date | 2009-05-18 | |
| dc.date.accessioned | 2026-07-07T13:15:19Z | |
| dc.date.available | 2026-07-07T13:15:19Z | |
| dc.description | In 1970, Walkup completely described the set of $f$-vectors for the four 3-manifolds $S^3$, $S^2 twist S^1$, $S^2 \times S^1$, and $RP^3$. We improve one of Walkup's main restricting inequalities on the set of $f$-vectors of 3-manifolds. As a consequence of a bound by Novik and Swartz, we also derive a new lower bound on the number of vertices that are needed for a combinatorial $d$-manifold in terms of its $β_1$-coefficient, which partially settles a conjecture of Kühnel. Enumerative results and a search for small triangulations with bistellar flips allow us, in combination with the new bounds, to completely determine the set of $f$-vectors for twenty further 3-manifolds, that is, for the connected sums of sphere bundles $(S^2 \times S^1)^{# k}$ and twisted sphere bundles $(S^2 twist S^1)^{# k}$, where $k=2,3,4,5,6,7,8,10,11,14$. For many more 3-manifolds of different geometric types we provide small triangulations and a partial description of their set of $f$-vectors. Moreover, we show that the 3-manifold $RP^3 # RP^3$ has (at least) two different minimal $g$-vectors. | |
| dc.description | 33 pages, 2 figures, 14 tables, reference updated, to appear in The Electronic Journal of Combinatorics | |
| dc.identifier | https://arxiv.org/abs/0805.1144 | |
| dc.identifier | http://arxiv.org/abs/0805.1144 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/230438 | |
| dc.subject | Combinatorics | |
| dc.subject | Geometric Topology | |
| dc.subject | 57Q15; 52B05; 57N10; 57M50 | |
| dc.title | f-Vectors of 3-Manifolds | |
| dc.type | text |