自由和碎片填充长度
Free and fragmenting filling length
摘要：
群的有限表示的Cayley 2-复形中的边圈η的填充长度是最小整数L，使得存在η的组合零同伦通过长度至多为L的圈直到基点。我们引入类似的概念，其中的零同伦是不需要固定的基点，并在其中的收缩循环被允许分叉。我们展示的群体中，由此产生的填充不变量表现出显着不同的行为，填充长度的标准概念。我们还定义了相应的填充不变量的黎曼流形，并将我们的结果转化为这种设置。
英文摘要：
The filling length of an edge-circuit ηin the Cayley 2-complex of a finite presentation of a group is the least integer L such that there is a combinatorial null-homotopy of ηdown to a base point through loops of length at most L. We introduce similar notions in which the null-homotopy is not required to fix a basepoint, and in which the contracting loop is allowed to bifurcate. We exhibit groups 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.
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