On the topology of graph picture spaces |
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Authors: | Jeremy L. Martin |
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Affiliation: | School of Mathematics, University of Minnesota, Minneapolis, MN 55455-0488, USA |
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Abstract: | We study the space of pictures of a graph G in complex projective d-space. The main result is that the homology groups (with integer coefficients) of 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. |
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Keywords: | Primary 05C10 Secondary 05B35, 14N20, 52C35 |
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