On the Topology of Multigraph Picture Spaces
نویسنده
چکیده
Let G be a multigraph. We study the space X (G) of all pictures of G in complex projective d-space. The main result is that the homology groups (with integer coefficients) of X (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. In the case that the picture space is smooth (which is equivalent to an elementary combinatorial condition on G), we give a Borel presentation of its cohomology ring and relate the intersection theory on X (G) to the Schubert calculus on flag manifolds.
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