Article ID Journal Published Year Pages File Type
9518108 Advances in Mathematics 2005 27 Pages PDF
Abstract
We study the space Xd(G) of pictures of a graph G in complex projective d-space. The main result is that the homology groups (with integer coefficients) of Xd(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 d-parallel matroids studied in combinatorial rigidity theory. For certain special graphs called 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.
Related Topics
Physical Sciences and Engineering Mathematics Mathematics (General)
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