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Results tagged with cobordism
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user 493465
Cobordism is a fundamental equivalence relation on the class of compact manifolds of the same dimension, set up using the concept of the boundary of a manifold.
2
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Turning cocycles in cobordism into an inclusion or a fibering
By the classical Pontryagin-Thom construction, we know that the cobordism group $\Omega^n_U(X)$ is represented by cocyles
$$ M\hookrightarrow X\times \mathbb{R}^{2k}\rightarrow X,$$
where $M$ is a manifold …
- 171
5
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Geometric interpretation of pairing between bordism and cobordism
In page 448 of these notes, a pairing between bordism and cobordism
$$\langle \ ,\ \rangle: U^m(X)\otimes U_n(X)\rightarrow \Omega^U_{n-m}$$
is defined as follows. … I also would like to know is there any known conditions on when can a cobordism class $x\in U^m(X)$ could be represented by an embedding $M\hookrightarrow X$ (when $0\leq m\leq \mathrm{dim}X $), or a fiber …
- 171