This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

Tags were heavily modified to better represent problems.

AND:
OR:
NO:

Found problems: 1

2021 Alibaba Global Math Competition, 11
Tags: homology , manifold , boundary , topology , algebraic topology
Let $M$ be a compact orientable $2n$-manifold with boundary, where $n \ge 2$. Suppose that $H_0(M;\mathbb{Q}) \cong \mathbb{Q}$ and $H_i(M;\mathbb{Q})=0$ for $i>0$. Prove that the order of $H_{n-1}(\partial M; \mathbb{Z})$ is a square number.