most recent 30 from http://mathoverflow.net 2013-05-23T02:32:56Z http://mathoverflow.net/feeds/question/62958 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/62958/do-bistellar-flips-preserve-shellability manifold-destiny 2011-04-25T19:23:45Z 2011-04-25T19:49:07Z

<p>I notice there is a strong connection between shellability of simplicial complexes and bistellar flips on these complexes; in particular, adding in a new facet of a shelling induces a bistellar flip on the boundary.</p> <p>Is it always the case that bistellar flips preserve shellability of a complex? In other words, if I apply a bistellar flip to a shellable simplicial complex, is the resulting simplicial complex also shellable? If so, how can this be seen easily?</p>

http://mathoverflow.net/questions/62958/do-bistellar-flips-preserve-shellability/62960#62960 Sergey Melikhov 2011-04-25T19:49:07Z 2011-04-25T19:49:07Z

<p>Obviously not, because there exist non-shellable combinatorial spheres, but any combinatorial $n$-sphere is bistellar-equivalent to the boundary of the $(n+1)$-simplex.</p> <p>The observation you mentioned is also in the very end of <a href="http://www.math.uic.edu/~kauffman/Lickorish.pdf" rel="nofollow">Lickorish's paper</a></p>