2026-09-19T23:12:10Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/1129042026-06-17T14:44:06Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Alexander Postnikov.
Liu, Xue (Mathematician)
Massachusetts Institute of Technology. Department of Mathematics.
Massachusetts Institute of Technology. Department of Mathematics
2017-12-20T18:16:45Z
2017-12-20T18:16:45Z
2017
2017
http://hdl.handle.net/1721.1/112904
1015201875
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2017.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 53-54).
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.
by Gaku Liu.
Ph.D.
54 pages
eng
Massachusetts Institute of Technology
MIT theses are protected by copyright. They may be viewed, downloaded, or printed from this source but further reproduction or distribution in any format is prohibited without written permission.
http://dspace.mit.edu/handle/1721.1/7582
Mathematics.
The topology of Baues complexes and flip graphs
Thesis
application/pdf
Publication
unknown
unknown
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