
Free and fragmenting filling length
Martin Bridson and Tim Riley Journal of Algebra 307(1), pages 171–190, 2007 The filling length of an edgecircuit \eta in the Cayley 2complex of a finite presentation of a group is the minimal integer length L such that there is a combinatorial nullhomotopy of \eta down to a base point through loops of length at most L. We introduce similar notions in which the nullhomotopy is not required to fix a base point, and in which the contracting loop is allowed to bifurcate. We exhibit a group in which the resulting filling invariants exhibit dramatically different behaviour to the standard notion of filling length. We also define the corresponding filling invariants for Riemannian manifolds and translate our results to this setting.
