The topology of Baues complexes and flip graphs

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.

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Mathematics.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2017

Author dc:creator

• Liu, Xue (Mathematician)

Advisor dc:contributor.advisor

• Alexander Postnikov.

• Mathematics.

Statement dc:rights

• 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.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/112904

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/112904