The Circle Transfer and Cobordism Categories
The Circle Transfer and Cobordism Categories
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圆转移和共边范畴
DOI：
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发表时间：
2017
影响因子：
0.7
通讯作者：
Jeffrey Giansiracusa
中科院分区：
文献类型：
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作者：
Jeffrey Giansiracusa
摘要：在拓扑学中，圆转移$QSigma (LX_{hS^1})_+ o QLX_+$出现在多种情况下。在本文中，我们观察到这个映射可以被几何重新解释为0流形和1流形的协协范畴的态射。让吗?1(X)表示一维共范畴，设Circ(X)∧？1(X)表示对象为未参化圆的不相交并的子范畴。在S1中乘法得到一个函子Circ(X)→Circ(LX)，这个函子与Circ（LX）的组合成？1（LX）与圆传递是同伦的。作为一个推论，我们描述了柱体的子范畴包含在二维共色范畴？2(X)并求出当X是一个点时它是零同伦的。
Abstract The circle transfer $QSigma (LX_{hS^1})_+ o QLX_+$ has appeared in several contexts in topology. In this note, we observe that this map admits a geometric re-interpretation as a morphism of cobordism categories of 0-manifolds and 1-cobordisms. Let ?1(X) denote the one-dimensional cobordism category and let Circ(X) ⊂ ?1(X) denote the subcategory whose objects are disjoint unions of unparametrized circles. Multiplication in S1 induces a functor Circ(X) → Circ(LX), and the composition of this functor with the inclusion of Circ(LX) into ?1(LX) is homotopic to the circle transfer. As a corollary, we describe the inclusion of the subcategory of cylinders into the two-dimensional cobordism category ?2(X) and find that it is null-homotopic when X is a point.