Suppose $M$ is a compact connected manifold-with-boundary with non-empty boundary. What can be said on whether $M$ can be given a CW complex structure?

A similar problem has been discussed for compact connected manifolds (i.e. with empty boundary) here, where it is true for $\dim \neq 4$ and not known for $\dim = 4$. Suppose the case for $\dim = 4$ is also shown true someday. Can the case with non-empty boundary be reduced to the case with empty boundary; i.e. are these problems equivalent?


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.