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A counterexample to the extension space conjecture for realizable oriented matroids

Geometric and topological combinatorics: Modern techniques and methods October 09, 2017 - October 13, 2017

October 09, 2017 (11:00 AM PDT - 12:00 PM PDT)
Speaker(s): Xue (Gaku) Liu (Max-Planck-Institut für Mathematik in den Naturwissenschaften)
Location: MSRI: Simons Auditorium
Tags/Keywords
  • oriented matroids

  • zonotopes

  • poset topology

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

2-Liu

Abstract

The extension space conjecture, proposed by Sturmfels and Ziegler in 1993, is a conjecture about the topology of a realizable oriented matroid's "extension space", which is a topological model for the set of all extensions of the oriented matroid by a single element. Equivalently, it is a conjecture about the poset of proper zonotopal tilings of a zonotope, namely that this poset is homotopy equivalent to a sphere. In this talk we describe a counterexample to this conjecture in three dimensions.

Supplements
29700?type=thumb Liu Notes 256 KB application/pdf Download
Video/Audio Files

2-Liu

H.264 Video 2-Liu.mp4 117 MB video/mp4 rtsp://videos.msri.org/data/000/029/565/original/2-Liu.mp4 Download
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