At title goes, I read the following lemma in Bredon's book (GTM139 Topology and Geometry Page 189). But I find that I have never seen it in any other texts on algebraic topology or homological algebra. So I would like to ask the references for it.

enter image description here

  • 1
    $\begingroup$ To add to Paul Frost's references, this is §26, Exer. 1 in Elements of algebraic topology by Munkres, although it is left as an exercise. You can also try to prove this lemma using spectral sequences like I did, but it doesn't seem very straightforward. $\endgroup$ Aug 23, 2018 at 0:29

1 Answer 1



Wall, C. T. C. "On the exactness of interlocking sequences." Enseignement math 12 (1966): 95-100


Hardie, K. A., and K. H. Kamps. "Exact sequence interlocking and free homotopy theory." Cahiers de topologie et géométrie différentielle catégoriques 26.1 (1985): 3-31



Your Answer

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

Not the answer you're looking for? Browse other questions tagged or ask your own question.