On the topology of graph picture spaces
| dc.creator | Martin, Jeremy L. | |
| dc.date | 2003-07-31 | |
| dc.date | 2004-04-28 | |
| dc.date.accessioned | 2026-07-07T04:59:59Z | |
| dc.date.available | 2026-07-07T04:59:59Z | |
| dc.description | We study the space ${\mathcal X}^{d}(G)$ of pictures of a graph $G$ in complex projective $d$-space. The main result is that the homology groups (with integer coefficients) of ${\mathcal X}^{d}(G)$ are completely determined by the Tutte polynomial of $G$. One application is a criterion in terms of the Tutte polynomial for independence in the {\it $d$-parallel matroids} studied in combinatorial rigidity theory. For certain special graphs called \defterm{orchards}, the picture space is smooth and has the structure of an iterated projective bundle. We give a Borel presentation of the cohomology ring of the picture space of an orchard, and use this presentation to develop an analogue of the classical Schubert calculus. | |
| dc.description | LaTeX (uses xypic package), 22 pages. Final version, to appear in Advances in Mathematics. The title has been changed slightly, the exposition improved, the material in Section 6 clarified, and some open problems added | |
| dc.identifier | https://arxiv.org/abs/math/0307405 | |
| dc.identifier | http://arxiv.org/abs/math/0307405 | |
| dc.identifier | Adv. Math. 191, no. 2 (2005), 312--338 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68219 | |
| dc.subject | Combinatorics | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Algebraic Topology | |
| dc.subject | 05C10 (Primary) 05B35, 14N20, 52C35 (Secondary) | |
| dc.title | On the topology of graph picture spaces | |
| dc.type | text |