Let $X$ be a connected graph, and $T$ its maximal tree. Via covering spaces and deck-transformations, how one can prove that $\pi_1(X)= \pi_1(X/T)$?
2026-03-30 20:54:11.1774904051
fundamental group of a graph is free
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Without using them you know that a tree is contractible and thus you get your thesis since $X\to X/T$ is an homotopy equivalence (it's the quotient modulo a contractible subcomplex).