oriented cobordism

Two oriented $n$ -manifolds $M$ and $M^{\\prime}$ are called cobordant if there is an oriented $n+1$ manifold with boundary $N$ such that $\\partial N=M\\coprod M^{\\prime opp}$ where $M^{\\prime opp}$ is $M^{\\prime}$ with orientation reversed. The triple $(N,M,M^{\\prime})$ is called a oriented cobordism. Cobordism is an equivalence relation, and a very coarse invariant of manifolds. For example, all surfaces are cobordant to the empty set (and hence to each other).

There is a cobordism category, where the objects are manifolds, and the morphisms are cobordisms between them. This category is important in topological .

单词	OrientedCobordism
释义	oriented cobordism Two oriented $n$ -manifolds $M$ and $M^{\\prime}$ are called cobordant if there is an oriented $n+1$ manifold with boundary $N$ such that $\\partial N=M\\coprod M^{\\prime opp}$ where $M^{\\prime opp}$ is $M^{\\prime}$ with orientation reversed. The triple $(N,M,M^{\\prime})$ is called a oriented cobordism. Cobordism is an equivalence relation, and a very coarse invariant of manifolds. For example, all surfaces are cobordant to the empty set (and hence to each other). There is a cobordism category, where the objects are manifolds, and the morphisms are cobordisms between them. This category is important in topological .
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