垂直3-流形的余边范畴与交积结构
Cobordism category of plumbed 3-manifolds and intersection product structures
摘要：
本文引入一类具有一定代数态射的分次交换环，研究了垂直3-流形的配边范畴。特别是，我们定义了一个非结合分配代数，给出了必要条件的抽象态射之间的同调的两个铅垂3-流形几何实现的协边。本文还考虑了同调配边幺半群，利用w-不变量给出了同调3-球面属于某个同调3-球面所对应的惯性群的必要条件.
英文摘要：
In this paper, we introduce a category of graded commutative rings with certain algebraic morphisms, to investigate the cobordism category of plumbed 3-manifolds. In particular, we define a non-associative distributive algebra that gives necessary conditions for an abstract morphism between the homologies of two plumbed 3-manifolds to be realized geometrically by a cobordism. Here we also consider the homology cobordism monoid, and give a necessary condition using w-invariants for the homology 3-spheres to belong to the inertia group associated to some homology 3-spheres.
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