Let \(\Delta ^n\) be the \(n\)-simplex with its usual \(\Delta \)-complex structure. Find all subcomplexes \(X\) of \(\Delta ^n\) such that \(\tilde {H}_{n-1}(X)\) is non-zero.
Question
Math 6520 • Algebraic Topology
Summer 2023 • Question 3
Question
Summer 2023 • Question 3
Let \(\Delta ^n\) be the \(n\)-simplex with its usual \(\Delta \)-complex structure. Find all subcomplexes \(X\) of \(\Delta ^n\) such that \(\tilde {H}_{n-1}(X)\) is non-zero.