I'm going to make a talk around higher homotopy groups, and the long exact sequence of relative homotopy groups. I would like to show some nice examples and applications of this theorem after the proof, can someone show/link me some of them?
Thanks!
2026-05-14 16:13:02.1778775182
Long Exact sequence of Relative Homotopy Groups: examples and applications
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There are applications in the book partially titled Nonabelian Algebraic Topology (pdf available there) and lots of history and intuition. The lower dimensional case
$$\partial: \pi_2(X,A,x) \to \pi_1(A,x)$$
has good applications to group theory (identities among relations).
Various presentations on my preprint page (e.g. the Galway talk) give other relations with algebraic topology.