![Top: the short exact sequence (3.17b) of A tmf -modules. Lower left:... | Download Scientific Diagram Top: the short exact sequence (3.17b) of A tmf -modules. Lower left:... | Download Scientific Diagram](https://www.researchgate.net/publication/370494786/figure/fig2/AS:11431281155383769@1683169361916/Top-the-short-exact-sequence-317b-of-A-tmf-modules-Lower-left-the-induced-long.png)
Top: the short exact sequence (3.17b) of A tmf -modules. Lower left:... | Download Scientific Diagram
![Sam Walters ☕️ on Twitter: "The long long long exact sequence of homotopy groups is immensely useful for computing (and relating) homotopy groups of complicated topological spaces in terms of those of Sam Walters ☕️ on Twitter: "The long long long exact sequence of homotopy groups is immensely useful for computing (and relating) homotopy groups of complicated topological spaces in terms of those of](https://pbs.twimg.com/media/E9I2UHNVIAA8MOx.jpg)
Sam Walters ☕️ on Twitter: "The long long long exact sequence of homotopy groups is immensely useful for computing (and relating) homotopy groups of complicated topological spaces in terms of those of
![D. Zack Garza on Twitter: "And now the beautiful machinery of homological algebra kicks in for us: by the Snake Lemma, any short exact sequence of chain complexes will induce a *long* D. Zack Garza on Twitter: "And now the beautiful machinery of homological algebra kicks in for us: by the Snake Lemma, any short exact sequence of chain complexes will induce a *long*](https://pbs.twimg.com/media/EZc_ypcWsAAIhQZ.png)
D. Zack Garza on Twitter: "And now the beautiful machinery of homological algebra kicks in for us: by the Snake Lemma, any short exact sequence of chain complexes will induce a *long*
Obvious Lemma: 0 → C n(A) −→ Cn(X) −→ Cn(X, A) → 0 is a short exact sequence. Thus this short exact sequence induces
![algebraic topology - Long exact sequence for a triple follows from long exact sequence for a pair? - Mathematics Stack Exchange algebraic topology - Long exact sequence for a triple follows from long exact sequence for a pair? - Mathematics Stack Exchange](https://i.stack.imgur.com/IUs4G.png)