Collapsing Simplicial Complexes
Abstract: Collapsing a simplicial complex is a combinatorial analog of contracting a space to a point. However, the two notions are not equivalent. For example, there are triangulations of the 3-ball that do not collapse. Understanding the conditions under which a simplicial complex collapses is a central issue in a number of problems in topology (and combinatorics), including the Poincare conjecture. In my talk I will use a combinatorial version of Morse theory to establish some geometric conditions that imply the collapsibility of some simplicial complexes.