This is joint work with Hoffman and Paquette.We describe the vanishing threshold for integer homology in Bernoulli random d-dimensional simplicial complexes, answering a 2003 question of Linial and Meshulam. Our bound is tight, up to a constant factor.The argument is fundamentally different, and surprisingly much simpler, than earlier arguments ...
Creator:
Kahle, Matthew (The Ohio State University)
Created:
2013-10-09
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
(This is work in progress with Dominic Dotterrer and Larry Guth.)In a graph, the girth is the length of the smallest cycle. How largethe girth can be for a graph on n vertices and m edges is a very wellstudied problem in combinatorics. More generally, in a d-dimensionalsimplicial complex, we define the d-systole to be the smallestnonempty collec...
Creator:
Kahle, Matthew (The Ohio State University)
Created:
2014-04-29
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.