Let \( X \) and \( Y \) be closed manifolds, and suppose \( X \) is a cover of \( Y \).

 Prove or disprove that the induced map on the first homology is injective.

The best solution was submitted by 신민규 (수리과학과 24학번, +4). Congratulations!

Here is the best solution of problem 2025-07.

Other solutions were submitted by 김동훈 (수리과학과 22학번, +3), Anar Rzayev (수리과학과 19학번, +3).