The topology of Baues complexes and flip graphs
Author(s)
Liu, Xue (Mathematician)
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Other Contributors
Massachusetts Institute of Technology. Department of Mathematics.
Advisor
Alexander Postnikov.
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This thesis contains several results on the connectedness of Baues complexes and flip graphs, which are topological spaces modeling certain sets coming from geometric combinatorics. These sets include the triangulations of a polytope, the tilings of a zonotope, and the extensions of an oriented matroid. Some long-standing conjectures are resolved, including the connectedness of triangulations of a product of two simplices and the sphericity of extension spaces of realizable oriented matroids. This thesis covers the main construction which is common to these proofs, but defers the details specific to each problem to other papers.
Description
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2017. Cataloged from PDF version of thesis. Includes bibliographical references (pages 53-54).
Date issued
2017Department
Massachusetts Institute of Technology. Department of MathematicsPublisher
Massachusetts Institute of Technology
Keywords
Mathematics.