Sign up ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Let $E \subset \mathbb R^n$. Must the homology groups $H_k (E)$ be trivial for $k \geq n$? How about just for $k > n$? If not, whats an example?


share|cite|improve this question
What have you tried so far? –  Jesse Madnick Dec 28 '11 at 4:34
Your question is answered here: –  Ryan Budney Dec 28 '11 at 4:55
@Ryan: Nice counterexample! I would have thought that the ‘dimension’ of a subspace would be bounded by the ‘dimension’ of the space, but I guess pathological subspaces can behave badly... –  Zhen Lin Dec 28 '11 at 6:00
@Ryan: are there also counterexamples for $k>n$? are the higher singular homology groups of the (n-1)-Hawaian earring known? –  user17786 Dec 28 '11 at 8:16

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.