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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.

13 votes
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Does the bordism homology theory satisfy the weak equivalence axiom?

Given bordism classes $g_0:M_0\to X$, $g_1:M_1\to X$ in $X$ and a cobordism $g:M\to Y$ ($\partial M=M_0\coprod M_1$) between $f\circ g_0$ and $f\circ g_1$, we need to find a cobordism $g':M\to X$ between …
Ricardo Andrade's user avatar
7 votes
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Does the signature admit a homotopy coherent refinement?

[Since my comment above appears to have been helpful, I am repeating it here.] I must admit I am unfamiliar with L-theory. Nevertheless, I came across a recent article on the arXiv which is related: …
Ricardo Andrade's user avatar