Take the 2-minute tour ×
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.

My question is about what one could say about the betti number of both spaces X and Y relatively to each other if we have a map f between them (eg. a classical case is when f is a covering map) is there an inequality if f happens to be injective or surjective?

Thank you in advance

share|improve this question
related: math.stackexchange.com/questions/41451/… –  Grigory M May 29 '11 at 8:52
Thanks Grigory, the answer was interesting it says that if the map is injective with a section then it induces an injective map of homology modules which means that the betti numbers of X are less or equal to those of Y. I am wondering if there is an answer to my question in a more general setting. –  El Moro May 29 '11 at 8:57
The morale from the linked question: injectivity/surjectivity of $f$ implies no inequality for Betty numbers whatsoever. So it's not quite clear what kind of answer you expect. –  Grigory M May 29 '11 at 9:02
I am actually looking for those special cases (like the one you mentioned with a section) in which one could compare betti numbers. –  El Moro May 29 '11 at 9:03

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.